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Helly's Theorem
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Helly''s theorem is a basic result in discrete geometry describing the ways that convex sets may intersect each other. It was discovered by Eduard Helly in 1913, but not published by him until 1923, by which time alternative proofs by Radon (1921) and König (1922) had already appeared. Helly''s theorem gave rise to the notion of a Helly family.We prove the finite version, using Radon''s theorem as in the proof by Radon (1921). The infinite version then follows by the finite intersection property characterization of compactness: a collection of closed subsets of a compact space has a non-empty intersection if and only if every finite subcollection has a non-empty intersection (once you fix a single set, the intersection of all others with it are closed subsets of a fixed compact space).
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131217968
- Editor Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
- Größe H220mm x B220mm
- EAN 9786131217968
- Format Fachbuch
- Titel Helly's Theorem
- Herausgeber Betascript Publishing
- Anzahl Seiten 64
- Genre Mathematik
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