Basic Properties of Convex Sets
Identifieur interne : 000322 ( Main/Exploration ); précédent : 000321; suivant : 000323Basic Properties of Convex Sets
Auteurs : Jean Gallier [États-Unis]Source :
- Texts in Applied Mathematics [ 0939-2475 ] ; 2011.
Abstract
Abstract: Convex sets play a very important role in geometry. In this chapter we state and prove some of the “classics” of convex affine geometry: Carath’eodory’s theorem, Radon’s theorem, Helly’s theorem, and Krein and Millman’s theorem. These theorems share the property that they are easy to state, but they are deep, and their proof, although rather short, requires a lot of creativity. We introduce the notions of separating and supporting hyperplanes, of vertices, and of extreme points. We also define centerpoints and prove their existence.
Url:
DOI: 10.1007/978-1-4419-9961-0_3
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 002194
- to stream Istex, to step Curation: 002194
- to stream Istex, to step Checkpoint: 000283
- to stream Main, to step Merge: 000322
- to stream Main, to step Curation: 000322
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Basic Properties of Convex Sets</title><author><name sortKey="Gallier, Jean" sort="Gallier, Jean" uniqKey="Gallier J" first="Jean" last="Gallier">Jean Gallier</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:A5D488EE8D0D473221F4C5B0FD9598ED9FC3BB2B</idno><date when="2011" year="2011">2011</date><idno type="doi">10.1007/978-1-4419-9961-0_3</idno><idno type="url">https://api.istex.fr/document/A5D488EE8D0D473221F4C5B0FD9598ED9FC3BB2B/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">002194</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">002194</idno><idno type="wicri:Area/Istex/Curation">002194</idno><idno type="wicri:Area/Istex/Checkpoint">000283</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000283</idno><idno type="wicri:doubleKey">0939-2475:2011:Gallier J:basic:properties:of</idno><idno type="wicri:Area/Main/Merge">000322</idno><idno type="wicri:Area/Main/Curation">000322</idno><idno type="wicri:Area/Main/Exploration">000322</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Basic Properties of Convex Sets</title><author><name sortKey="Gallier, Jean" sort="Gallier, Jean" uniqKey="Gallier J" first="Jean" last="Gallier">Jean Gallier</name><affiliation wicri:level="2"><country xml:lang="fr">États-Unis</country><wicri:regionArea>Department of Computer and Information Science, University of Pennsylvania, 3330 Walnut Street, 19104, Philadelphia, PA</wicri:regionArea><placeName><region type="state">Pennsylvanie</region></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">États-Unis</country></affiliation></author></analytic><monogr></monogr><series><title level="s">Texts in Applied Mathematics</title><imprint><date>2011</date></imprint><idno type="ISSN">0939-2475</idno><idno type="ISSN">0939-2475</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0939-2475</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Convex sets play a very important role in geometry. In this chapter we state and prove some of the “classics” of convex affine geometry: Carath’eodory’s theorem, Radon’s theorem, Helly’s theorem, and Krein and Millman’s theorem. These theorems share the property that they are easy to state, but they are deep, and their proof, although rather short, requires a lot of creativity. We introduce the notions of separating and supporting hyperplanes, of vertices, and of extreme points. We also define centerpoints and prove their existence.</div></front></TEI><affiliations><list><country><li>États-Unis</li></country><region><li>Pennsylvanie</li></region></list><tree><country name="États-Unis"><region name="Pennsylvanie"><name sortKey="Gallier, Jean" sort="Gallier, Jean" uniqKey="Gallier J" first="Jean" last="Gallier">Jean Gallier</name></region><name sortKey="Gallier, Jean" sort="Gallier, Jean" uniqKey="Gallier J" first="Jean" last="Gallier">Jean Gallier</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000322 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000322 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Mathematiques
|area= BourbakiV1
|flux= Main
|étape= Exploration
|type= RBID
|clé= ISTEX:A5D488EE8D0D473221F4C5B0FD9598ED9FC3BB2B
|texte= Basic Properties of Convex Sets
}}
| This area was generated with Dilib version V0.6.33. |  |