H
Identifieur interne : 002C18 ( Istex/Corpus ); précédent : 002C17; suivant : 002C19H
Auteurs : V. I. Ponomarev ; Yu. B. Rudyak ; A. F. Kharshiladze ; Yu. N. Subbotin ; D. P. Zhelobenko ; A. I. Shtern ; B. I. Golubov ; S. A. Rukova ; E. D. Solomentsev ; O. A. Ivanova ; I. A. Aleksandrov ; P. S. Soltan ; V. I. Sobolev ; A. V. Prokhorov ; I. V. Dolgachev ; V. V. Rumyantsev ; I. B. Vapnyarski ; V. D. Mazurov ; V. M. Tikhomirov ; L. P. Kuptsov ; D. V. Anosov ; V. A. Yakubovich ; B. V. Khvedelidze ; S. V. Matveev ; P. I. Lizorkin ; S. V. Shvedenko ; L. D. Kudryavtsev ; B. M. Bredikhin ; A. A. Konyushkov ; Yu. A. Brychkov ; A. P. Prudnikov ; E. M. Nikishin ; E. A. Gorin ; E. A. Grebennikov ; A. B. Ivanov ; A. L. Onishchik ; P. M. Tamrazov ; V. F. Emel Anov ; A. I. Barabanov ; Yu. A. Rozanov ; L. I. Kamynin ; V. A. Skvortsov ; E. M. Chirka ; E. B. Vinberg ; Yu. G. Zarkhin ; I. G. Koshevnikova ; R. A. Minlos ; M. I. Vo Tsekhovski ; A. G. El In ; A. V. Arkhangel Ki ; I. I. Volkov ; E. M. SemenovSource :
- Encyclopaedia of Mathematics ; 1995.
Abstract
Abstract: A Hausdorff space which, under any topological imbedding into an arbitrary Hausdorff space Y, is a closed set in Y. The characteristic property of an H-closed space is that any open covering of the space contains a finite subfamily the closures of the elements of which cover the space. A regular H-closed space is compact. If every closed subspace of a space is H-closed, then the space itself is compact. A theory has been developed for H-closed extensions of Hausdorff spaces.
Url:
DOI: 10.1007/978-1-4899-3795-7_6
Links to Exploration step
ISTEX:D6FEBBE5C50BD0A5703ABBA569194B05CCD8F84ALe document en format XML
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Shtern</name></author><author><name sortKey="Golubov, B I" sort="Golubov, B I" uniqKey="Golubov B" first="B. I." last="Golubov">B. I. Golubov</name></author><author><name sortKey="Rukova, S A" sort="Rukova, S A" uniqKey="Rukova S" first="S. A." last="Rukova">S. A. Rukova</name></author><author><name sortKey="Solomentsev, E D" sort="Solomentsev, E D" uniqKey="Solomentsev E" first="E. D." last="Solomentsev">E. D. Solomentsev</name></author><author><name sortKey="Ivanova, O A" sort="Ivanova, O A" uniqKey="Ivanova O" first="O. A." last="Ivanova">O. A. Ivanova</name></author><author><name sortKey="Aleksandrov, I A" sort="Aleksandrov, I A" uniqKey="Aleksandrov I" first="I. A." last="Aleksandrov">I. A. Aleksandrov</name></author><author><name sortKey="Soltan, P S" sort="Soltan, P S" uniqKey="Soltan P" first="P. S." last="Soltan">P. S. Soltan</name></author><author><name sortKey="Sobolev, V I" sort="Sobolev, V I" uniqKey="Sobolev V" first="V. I." last="Sobolev">V. I. Sobolev</name></author><author><name sortKey="Prokhorov, A V" sort="Prokhorov, A V" uniqKey="Prokhorov A" first="A. V." last="Prokhorov">A. V. Prokhorov</name></author><author><name sortKey="Dolgachev, I V" sort="Dolgachev, I V" uniqKey="Dolgachev I" first="I. V." last="Dolgachev">I. V. Dolgachev</name></author><author><name sortKey="Rumyantsev, V V" sort="Rumyantsev, V V" uniqKey="Rumyantsev V" first="V. V." last="Rumyantsev">V. V. Rumyantsev</name></author><author><name sortKey="Vapnyarski, I B" sort="Vapnyarski, I B" uniqKey="Vapnyarski I" first="I. B." last="Vapnyarski">I. B. Vapnyarski</name></author><author><name sortKey="Mazurov, V D" sort="Mazurov, V D" uniqKey="Mazurov V" first="V. D." last="Mazurov">V. D. Mazurov</name></author><author><name sortKey="Tikhomirov, V M" sort="Tikhomirov, V M" uniqKey="Tikhomirov V" first="V. M." last="Tikhomirov">V. M. Tikhomirov</name></author><author><name sortKey="Kuptsov, L P" sort="Kuptsov, L P" uniqKey="Kuptsov L" first="L. P." last="Kuptsov">L. P. Kuptsov</name></author><author><name sortKey="Anosov, D V" sort="Anosov, D V" uniqKey="Anosov D" first="D. V." last="Anosov">D. V. Anosov</name></author><author><name sortKey="Yakubovich, V A" sort="Yakubovich, V A" uniqKey="Yakubovich V" first="V. A." last="Yakubovich">V. A. Yakubovich</name></author><author><name sortKey="Khvedelidze, B V" sort="Khvedelidze, B V" uniqKey="Khvedelidze B" first="B. V." last="Khvedelidze">B. V. Khvedelidze</name></author><author><name sortKey="Matveev, S V" sort="Matveev, S V" uniqKey="Matveev S" first="S. V." last="Matveev">S. V. Matveev</name></author><author><name sortKey="Lizorkin, P I" sort="Lizorkin, P I" uniqKey="Lizorkin P" first="P. I." last="Lizorkin">P. I. Lizorkin</name></author><author><name sortKey="Shvedenko, S V" sort="Shvedenko, S V" uniqKey="Shvedenko S" first="S. V." last="Shvedenko">S. V. Shvedenko</name></author><author><name sortKey="Kudryavtsev, L D" sort="Kudryavtsev, L D" uniqKey="Kudryavtsev L" first="L. D." last="Kudryavtsev">L. D. Kudryavtsev</name></author><author><name sortKey="Bredikhin, B M" sort="Bredikhin, B M" uniqKey="Bredikhin B" first="B. M." last="Bredikhin">B. M. Bredikhin</name></author><author><name sortKey="Konyushkov, A A" sort="Konyushkov, A A" uniqKey="Konyushkov A" first="A. A." last="Konyushkov">A. A. Konyushkov</name></author><author><name sortKey="Brychkov, Yu A" sort="Brychkov, Yu A" uniqKey="Brychkov Y" first="Yu. A." last="Brychkov">Yu. A. Brychkov</name></author><author><name sortKey="Prudnikov, A P" sort="Prudnikov, A P" uniqKey="Prudnikov A" first="A. P." last="Prudnikov">A. P. Prudnikov</name></author><author><name sortKey="Nikishin, E M" sort="Nikishin, E M" uniqKey="Nikishin E" first="E. M." last="Nikishin">E. M. Nikishin</name></author><author><name sortKey="Gorin, E A" sort="Gorin, E A" uniqKey="Gorin E" first="E. A." last="Gorin">E. A. Gorin</name></author><author><name sortKey="Grebennikov, E A" sort="Grebennikov, E A" uniqKey="Grebennikov E" first="E. A." last="Grebennikov">E. A. Grebennikov</name></author><author><name sortKey="Ivanov, A B" sort="Ivanov, A B" uniqKey="Ivanov A" first="A. B." last="Ivanov">A. B. Ivanov</name></author><author><name sortKey="Onishchik, A L" sort="Onishchik, A L" uniqKey="Onishchik A" first="A. L." last="Onishchik">A. L. Onishchik</name></author><author><name sortKey="Tamrazov, P M" sort="Tamrazov, P M" uniqKey="Tamrazov P" first="P. M." last="Tamrazov">P. M. Tamrazov</name></author><author><name sortKey="Emel Anov, V F" sort="Emel Anov, V F" uniqKey="Emel Anov V" first="V. F." last="Emel Anov">V. F. Emel Anov</name></author><author><name sortKey="Barabanov, A I" sort="Barabanov, A I" uniqKey="Barabanov A" first="A. I." last="Barabanov">A. I. Barabanov</name></author><author><name sortKey="Rozanov, Yu A" sort="Rozanov, Yu A" uniqKey="Rozanov Y" first="Yu. A." last="Rozanov">Yu. A. Rozanov</name></author><author><name sortKey="Kamynin, L I" sort="Kamynin, L I" uniqKey="Kamynin L" first="L. I." last="Kamynin">L. I. Kamynin</name></author><author><name sortKey="Skvortsov, V A" sort="Skvortsov, V A" uniqKey="Skvortsov V" first="V. A." last="Skvortsov">V. A. Skvortsov</name></author><author><name sortKey="Chirka, E M" sort="Chirka, E M" uniqKey="Chirka E" first="E. M." last="Chirka">E. M. Chirka</name></author><author><name sortKey="Vinberg, E B" sort="Vinberg, E B" uniqKey="Vinberg E" first="E. B." last="Vinberg">E. B. Vinberg</name></author><author><name sortKey="Zarkhin, Yu G" sort="Zarkhin, Yu G" uniqKey="Zarkhin Y" first="Yu. G." last="Zarkhin">Yu. G. Zarkhin</name></author><author><name sortKey="Koshevnikova, I G" sort="Koshevnikova, I G" uniqKey="Koshevnikova I" first="I. G." last="Koshevnikova">I. G. Koshevnikova</name></author><author><name sortKey="Minlos, R A" sort="Minlos, R A" uniqKey="Minlos R" first="R. A." last="Minlos">R. A. Minlos</name></author><author><name sortKey="Vo Tsekhovski, M I" sort="Vo Tsekhovski, M I" uniqKey="Vo Tsekhovski M" first="M. I." last="Vo Tsekhovski">M. I. Vo Tsekhovski</name></author><author><name sortKey="El In, A G" sort="El In, A G" uniqKey="El In A" first="A. G." last="El In">A. G. El In</name></author><author><name sortKey="Arkhangel Ki, A V" sort="Arkhangel Ki, A V" uniqKey="Arkhangel Ki A" first="A. V." last="Arkhangel Ki">A. V. Arkhangel Ki</name></author><author><name sortKey="Volkov, I I" sort="Volkov, I I" uniqKey="Volkov I" first="I. I." last="Volkov">I. I. Volkov</name></author><author><name sortKey="Semenov, E M" sort="Semenov, E M" uniqKey="Semenov E" first="E. M." last="Semenov">E. M. Semenov</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:D6FEBBE5C50BD0A5703ABBA569194B05CCD8F84A</idno><date when="1995" year="1995">1995</date><idno type="doi">10.1007/978-1-4899-3795-7_6</idno><idno type="url">https://api.istex.fr/document/D6FEBBE5C50BD0A5703ABBA569194B05CCD8F84A/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">002C18</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">002C18</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">H</title><author><name sortKey="Ponomarev, V I" sort="Ponomarev, V I" uniqKey="Ponomarev V" first="V. I." last="Ponomarev">V. I. Ponomarev</name></author><author><name sortKey="Rudyak, Yu B" sort="Rudyak, Yu B" uniqKey="Rudyak Y" first="Yu. B." last="Rudyak">Yu. B. Rudyak</name></author><author><name sortKey="Kharshiladze, A F" sort="Kharshiladze, A F" uniqKey="Kharshiladze A" first="A. F." last="Kharshiladze">A. F. Kharshiladze</name></author><author><name sortKey="Subbotin, Yu N" sort="Subbotin, Yu N" uniqKey="Subbotin Y" first="Yu. N." last="Subbotin">Yu. N. Subbotin</name></author><author><name sortKey="Zhelobenko, D P" sort="Zhelobenko, D P" uniqKey="Zhelobenko D" first="D. P." last="Zhelobenko">D. P. Zhelobenko</name></author><author><name sortKey="Shtern, A I" sort="Shtern, A I" uniqKey="Shtern A" first="A. I." last="Shtern">A. I. Shtern</name></author><author><name sortKey="Golubov, B I" sort="Golubov, B I" uniqKey="Golubov B" first="B. I." last="Golubov">B. I. Golubov</name></author><author><name sortKey="Rukova, S A" sort="Rukova, S A" uniqKey="Rukova S" first="S. A." last="Rukova">S. A. Rukova</name></author><author><name sortKey="Solomentsev, E D" sort="Solomentsev, E D" uniqKey="Solomentsev E" first="E. D." last="Solomentsev">E. D. Solomentsev</name></author><author><name sortKey="Ivanova, O A" sort="Ivanova, O A" uniqKey="Ivanova O" first="O. A." last="Ivanova">O. A. Ivanova</name></author><author><name sortKey="Aleksandrov, I A" sort="Aleksandrov, I A" uniqKey="Aleksandrov I" first="I. A." last="Aleksandrov">I. A. Aleksandrov</name></author><author><name sortKey="Soltan, P S" sort="Soltan, P S" uniqKey="Soltan P" first="P. S." last="Soltan">P. S. Soltan</name></author><author><name sortKey="Sobolev, V I" sort="Sobolev, V I" uniqKey="Sobolev V" first="V. I." last="Sobolev">V. I. Sobolev</name></author><author><name sortKey="Prokhorov, A V" sort="Prokhorov, A V" uniqKey="Prokhorov A" first="A. V." last="Prokhorov">A. V. Prokhorov</name></author><author><name sortKey="Dolgachev, I V" sort="Dolgachev, I V" uniqKey="Dolgachev I" first="I. V." last="Dolgachev">I. V. Dolgachev</name></author><author><name sortKey="Rumyantsev, V V" sort="Rumyantsev, V V" uniqKey="Rumyantsev V" first="V. V." last="Rumyantsev">V. V. Rumyantsev</name></author><author><name sortKey="Vapnyarski, I B" sort="Vapnyarski, I B" uniqKey="Vapnyarski I" first="I. B." last="Vapnyarski">I. B. Vapnyarski</name></author><author><name sortKey="Mazurov, V D" sort="Mazurov, V D" uniqKey="Mazurov V" first="V. D." last="Mazurov">V. D. Mazurov</name></author><author><name sortKey="Tikhomirov, V M" sort="Tikhomirov, V M" uniqKey="Tikhomirov V" first="V. M." last="Tikhomirov">V. M. Tikhomirov</name></author><author><name sortKey="Kuptsov, L P" sort="Kuptsov, L P" uniqKey="Kuptsov L" first="L. P." last="Kuptsov">L. P. Kuptsov</name></author><author><name sortKey="Anosov, D V" sort="Anosov, D V" uniqKey="Anosov D" first="D. V." last="Anosov">D. V. Anosov</name></author><author><name sortKey="Yakubovich, V A" sort="Yakubovich, V A" uniqKey="Yakubovich V" first="V. A." last="Yakubovich">V. A. Yakubovich</name></author><author><name sortKey="Khvedelidze, B V" sort="Khvedelidze, B V" uniqKey="Khvedelidze B" first="B. V." last="Khvedelidze">B. V. Khvedelidze</name></author><author><name sortKey="Matveev, S V" sort="Matveev, S V" uniqKey="Matveev S" first="S. V." last="Matveev">S. V. Matveev</name></author><author><name sortKey="Lizorkin, P I" sort="Lizorkin, P I" uniqKey="Lizorkin P" first="P. I." last="Lizorkin">P. I. Lizorkin</name></author><author><name sortKey="Shvedenko, S V" sort="Shvedenko, S V" uniqKey="Shvedenko S" first="S. V." last="Shvedenko">S. V. Shvedenko</name></author><author><name sortKey="Kudryavtsev, L D" sort="Kudryavtsev, L D" uniqKey="Kudryavtsev L" first="L. D." last="Kudryavtsev">L. D. Kudryavtsev</name></author><author><name sortKey="Bredikhin, B M" sort="Bredikhin, B M" uniqKey="Bredikhin B" first="B. M." last="Bredikhin">B. M. Bredikhin</name></author><author><name sortKey="Konyushkov, A A" sort="Konyushkov, A A" uniqKey="Konyushkov A" first="A. A." last="Konyushkov">A. A. Konyushkov</name></author><author><name sortKey="Brychkov, Yu A" sort="Brychkov, Yu A" uniqKey="Brychkov Y" first="Yu. A." last="Brychkov">Yu. A. Brychkov</name></author><author><name sortKey="Prudnikov, A P" sort="Prudnikov, A P" uniqKey="Prudnikov A" first="A. P." last="Prudnikov">A. P. Prudnikov</name></author><author><name sortKey="Nikishin, E M" sort="Nikishin, E M" uniqKey="Nikishin E" first="E. M." last="Nikishin">E. M. Nikishin</name></author><author><name sortKey="Gorin, E A" sort="Gorin, E A" uniqKey="Gorin E" first="E. A." last="Gorin">E. A. Gorin</name></author><author><name sortKey="Grebennikov, E A" sort="Grebennikov, E A" uniqKey="Grebennikov E" first="E. A." last="Grebennikov">E. A. Grebennikov</name></author><author><name sortKey="Ivanov, A B" sort="Ivanov, A B" uniqKey="Ivanov A" first="A. B." last="Ivanov">A. B. Ivanov</name></author><author><name sortKey="Onishchik, A L" sort="Onishchik, A L" uniqKey="Onishchik A" first="A. L." last="Onishchik">A. L. Onishchik</name></author><author><name sortKey="Tamrazov, P M" sort="Tamrazov, P M" uniqKey="Tamrazov P" first="P. M." last="Tamrazov">P. M. Tamrazov</name></author><author><name sortKey="Emel Anov, V F" sort="Emel Anov, V F" uniqKey="Emel Anov V" first="V. F." last="Emel Anov">V. F. Emel Anov</name></author><author><name sortKey="Barabanov, A I" sort="Barabanov, A I" uniqKey="Barabanov A" first="A. I." last="Barabanov">A. I. Barabanov</name></author><author><name sortKey="Rozanov, Yu A" sort="Rozanov, Yu A" uniqKey="Rozanov Y" first="Yu. A." last="Rozanov">Yu. A. Rozanov</name></author><author><name sortKey="Kamynin, L I" sort="Kamynin, L I" uniqKey="Kamynin L" first="L. I." last="Kamynin">L. I. Kamynin</name></author><author><name sortKey="Skvortsov, V A" sort="Skvortsov, V A" uniqKey="Skvortsov V" first="V. A." last="Skvortsov">V. A. Skvortsov</name></author><author><name sortKey="Chirka, E M" sort="Chirka, E M" uniqKey="Chirka E" first="E. M." last="Chirka">E. M. Chirka</name></author><author><name sortKey="Vinberg, E B" sort="Vinberg, E B" uniqKey="Vinberg E" first="E. B." last="Vinberg">E. B. Vinberg</name></author><author><name sortKey="Zarkhin, Yu G" sort="Zarkhin, Yu G" uniqKey="Zarkhin Y" first="Yu. G." last="Zarkhin">Yu. G. Zarkhin</name></author><author><name sortKey="Koshevnikova, I G" sort="Koshevnikova, I G" uniqKey="Koshevnikova I" first="I. G." last="Koshevnikova">I. G. Koshevnikova</name></author><author><name sortKey="Minlos, R A" sort="Minlos, R A" uniqKey="Minlos R" first="R. A." last="Minlos">R. A. Minlos</name></author><author><name sortKey="Vo Tsekhovski, M I" sort="Vo Tsekhovski, M I" uniqKey="Vo Tsekhovski M" first="M. I." last="Vo Tsekhovski">M. I. Vo Tsekhovski</name></author><author><name sortKey="El In, A G" sort="El In, A G" uniqKey="El In A" first="A. G." last="El In">A. G. El In</name></author><author><name sortKey="Arkhangel Ki, A V" sort="Arkhangel Ki, A V" uniqKey="Arkhangel Ki A" first="A. V." last="Arkhangel Ki">A. V. Arkhangel Ki</name></author><author><name sortKey="Volkov, I I" sort="Volkov, I I" uniqKey="Volkov I" first="I. I." last="Volkov">I. I. Volkov</name></author><author><name sortKey="Semenov, E M" sort="Semenov, E M" uniqKey="Semenov E" first="E. M." last="Semenov">E. M. Semenov</name></author></analytic><monogr></monogr><series><title level="s">Encyclopaedia of Mathematics</title><imprint><date>1995</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: A Hausdorff space which, under any topological imbedding into an arbitrary Hausdorff space Y, is a closed set in Y. The characteristic property of an H-closed space is that any open covering of the space contains a finite subfamily the closures of the elements of which cover the space. A regular H-closed space is compact. If every closed subspace of a space is H-closed, then the space itself is compact. A theory has been developed for H-closed extensions of Hausdorff spaces.</div></front></TEI><istex><corpusName>springer-ebooks</corpusName><author><json:item><name>V. I. Ponomarev</name></json:item><json:item><name>Yu. B. Rudyak</name></json:item><json:item><name>A. F. Kharshiladze</name></json:item><json:item><name>Yu. N. Subbotin</name></json:item><json:item><name>D. P. Zhelobenko</name></json:item><json:item><name>A. I. Shtern</name></json:item><json:item><name>B. I. Golubov</name></json:item><json:item><name>S. A. Rukova</name></json:item><json:item><name>E. D. Solomentsev</name></json:item><json:item><name>O. A. Ivanova</name></json:item><json:item><name>I. A. Aleksandrov</name></json:item><json:item><name>P. S. Soltan</name></json:item><json:item><name>V. I. Sobolev</name></json:item><json:item><name>A. V. Prokhorov</name></json:item><json:item><name>I. V. Dolgachev</name></json:item><json:item><name>V. V. Rumyantsev</name></json:item><json:item><name>I. B. Vapnyarskiĭ</name></json:item><json:item><name>V. D. Mazurov</name></json:item><json:item><name>V. M. Tikhomirov</name></json:item><json:item><name>L. P. Kuptsov</name></json:item><json:item><name>D. V. Anosov</name></json:item><json:item><name>V. A. Yakubovich</name></json:item><json:item><name>B. V. Khvedelidze</name></json:item><json:item><name>S. V. Matveev</name></json:item><json:item><name>P. I. Lizorkin</name></json:item><json:item><name>S. V. Shvedenko</name></json:item><json:item><name>L. D. Kudryavtsev</name></json:item><json:item><name>B. M. Bredikhin</name></json:item><json:item><name>A. A. Konyushkov</name></json:item><json:item><name>Yu. A. Brychkov</name></json:item><json:item><name>A. P. Prudnikov</name></json:item><json:item><name>E. M. Nikishin</name></json:item><json:item><name>E. A. Gorin</name></json:item><json:item><name>E. A. 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The characteristic property of an H-closed space is that any open covering of the space contains a finite subfamily the closures of the elements of which cover the space. A regular H-closed space is compact. If every closed subspace of a space is H-closed, then the space itself is compact. 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DisplayOrder="Western"><GivenName>I.</GivenName><GivenName>G.</GivenName><FamilyName>Koshevnikova</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>R.</GivenName><GivenName>A.</GivenName><FamilyName>Minlos</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>M.</GivenName><GivenName>I.</GivenName><FamilyName>Voĭtsekhovskiĭ</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>A.</GivenName><GivenName>G.</GivenName><FamilyName>El’kin</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>A.</GivenName><GivenName>V.</GivenName><FamilyName>Arkhangel’skiĭ</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>I.</GivenName><GivenName>I.</GivenName><FamilyName>Volkov</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>E.</GivenName><GivenName>M.</GivenName><FamilyName>Semenov</FamilyName></AuthorName></Author></AuthorGroup><Abstract ID="Abs1" Language="En" OutputMedium="Online"><Heading>Abstract</Heading><Para>A <Emphasis Type="Bold">Hausdorff space</Emphasis> which, under any topological imbedding into an arbitrary Hausdorff space <Emphasis Type="Italic">Y</Emphasis>, is a closed set in <Emphasis Type="Italic">Y</Emphasis>. The characteristic property of an <Emphasis Type="Italic">H</Emphasis>-closed space is that any open covering of the space contains a finite subfamily the closures of the elements of which cover the space. A regular <Emphasis Type="Italic">H</Emphasis>-closed space is compact. If every closed subspace of a space is <Emphasis Type="Italic">H</Emphasis>-closed, then the space itself is compact. A theory has been developed for <Emphasis Type="Italic">H</Emphasis>-closed extensions of Hausdorff spaces.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>H</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>H</title></titleInfo><name type="personal"><namePart type="given">V.</namePart><namePart type="given">I.</namePart><namePart type="family">Ponomarev</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Yu.</namePart><namePart type="given">B.</namePart><namePart type="family">Rudyak</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="given">F.</namePart><namePart type="family">Kharshiladze</namePart><role><roleTerm type="text">author</roleTerm></role></name><name 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type="personal"><namePart type="given">E.</namePart><namePart type="given">B.</namePart><namePart type="family">Vinberg</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Yu.</namePart><namePart type="given">G.</namePart><namePart type="family">Zarkhin</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">I.</namePart><namePart type="given">G.</namePart><namePart type="family">Koshevnikova</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">R.</namePart><namePart type="given">A.</namePart><namePart type="family">Minlos</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">M.</namePart><namePart type="given">I.</namePart><namePart type="family">Voĭtsekhovskiĭ</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="given">G.</namePart><namePart type="family">El’kin</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="given">V.</namePart><namePart type="family">Arkhangel’skiĭ</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">I.</namePart><namePart type="given">I.</namePart><namePart type="family">Volkov</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">E.</namePart><namePart type="given">M.</namePart><namePart type="family">Semenov</namePart><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="research-article" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Springer US</publisher><place><placeTerm type="text">Boston, MA</placeTerm></place><dateIssued encoding="w3cdtf">1995</dateIssued><dateIssued encoding="w3cdtf">1995</dateIssued><copyrightDate encoding="w3cdtf">1995</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: A Hausdorff space which, under any topological imbedding into an arbitrary Hausdorff space Y, is a closed set in Y. The characteristic property of an H-closed space is that any open covering of the space contains a finite subfamily the closures of the elements of which cover the space. A regular H-closed space is compact. If every closed subspace of a space is H-closed, then the space itself is compact. A theory has been developed for H-closed extensions of Hausdorff spaces.</abstract><relatedItem type="host"><titleInfo><title>Encyclopaedia of Mathematics</title><subTitle>Coproduct — Hausdorff — Young Inequalities</subTitle></titleInfo><name type="personal"><namePart type="given">M.</namePart><namePart type="family">Hazewinkel</namePart><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Contributed volume" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</genre><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">1995</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11649">Mathematics and Statistics</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="SCM">Mathematics</topic><topic authority="SpringerSubjectCodes" authorityURI="SCM00009">Mathematics, general</topic></subject><identifier type="DOI">10.1007/978-1-4899-3795-7</identifier><identifier type="ISBN">978-0-7923-2974-9</identifier><identifier type="eISBN">978-1-4899-3795-7</identifier><identifier type="BookTitleID">229604</identifier><identifier type="BookID">978-1-4899-3795-7</identifier><identifier type="BookChapterCount">6</identifier><identifier type="BookVolumeNumber">2</identifier><identifier type="BookSequenceNumber">0</identifier><part><date>1995</date><detail type="volume"><number>2</number><caption>vol.</caption></detail><extent unit="pages"><start>912</start><end>963</end></extent></part><recordInfo><recordOrigin>Springer Science+Business Media Dordrecht, 1995</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Encyclopaedia of Mathematics</title></titleInfo><name type="personal"><namePart type="given">M.</namePart><namePart type="family">Hazewinkel</namePart><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">1995</copyrightDate><issuance>serial</issuance></originInfo><identifier type="SeriesID">5920</identifier><recordInfo><recordOrigin>Springer Science+Business Media Dordrecht, 1995</recordOrigin></recordInfo></relatedItem><identifier type="istex">D6FEBBE5C50BD0A5703ABBA569194B05CCD8F84A</identifier><identifier type="ark">ark:/67375/HCB-ZKG993M0-V</identifier><identifier type="DOI">10.1007/978-1-4899-3795-7_6</identifier><identifier type="ChapterID">6</identifier><identifier type="ChapterID">Chap6</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer Science+Business Media Dordrecht, 1995</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-3XSW68JL-F">springer</recordContentSource><recordOrigin>Springer Science+Business Media Dordrecht, 1995</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/document/D6FEBBE5C50BD0A5703ABBA569194B05CCD8F84A/metadata/json</uri></json:item></metadata><annexes><json:item><extension>xml</extension><original>true</original><mimetype>application/xml</mimetype><uri>https://api.istex.fr/document/D6FEBBE5C50BD0A5703ABBA569194B05CCD8F84A/annexes/xml</uri></json:item></annexes></istex></record>Pour manipuler ce document sous Unix (Dilib)
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