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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Helly's theorem ： ウィキペディア英語版 Helly's theorem 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 and had already appeared. Helly's theorem gave rise to the notion of a Helly family. ==Statement== Let be a finite collection of convex subsets of , with . If the intersection of every of these sets is nonempty, then the whole collection has a nonempty intersection; that is, :$\backslash bigcap\_^n\; X\_j\backslash ne\backslash varnothing.$ For infinite collections one has to assume compactness: Let be a collection of compact convex subsets of , such that every subcollection of cardinality at most has nonempty intersection, then the whole collection has nonempty intersection. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Helly's theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.