翻訳と辞書 Words near each other ・ Katzrin ・ Katzrin ancient village and synagogue ・ Katzsohlbach ・ Katzsohlteich ・ Katzwang ・ Katzweiler ・ Katzwinkel ・ Katzwinkel, Vulkaneifel ・ Katz–Lang finiteness theorem ・ Katádfa ・ Kató Bárczy ・ Kató Havas ・ Kató Hámán ・ Kató Lomb ・ Katúň ・ Katětov–Tong insertion theorem ・ Katıralanı ・ Katō Danzō ・ Katō District ・ Katō District, Hokkaido ・ Katō District, Hyōgo ・ Katō Hiroyuki ・ Katō Kiyomasa ・ Katō Mitsuyasu ・ Katō Sadakichi ・ Katō Shrine ・ Katō Tadaaki ・ Katō Takaaki ・ Katō Tomosaburō ・ Katō Yasuaki Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Katětov–Tong insertion theorem ： ウィキペディア英語版 Katětov–Tong insertion theorem The Katětov–Tong insertion theorem is a theorem of point-set topology proved independently by Miroslav Katětov〔Miroslav Katětov, ''On real-valued functions in topological spaces'', Fundamenta Mathematicae 38 (1951), 85–91. ()〕 and Hing Tong〔Hing Tong, ''Some characterizations of normal and perfectly normal spaces'', Duke Mathematical Journal 19 (1952), 289–292. 〕 in the 1950s. The theorem states the following: Let $X$ be a normal topological space and let $g,\; h\backslash colon\; X\; \backslash to\; \backslash mathbb$ be functions with g upper semicontinuous, h lower semicontinuous and $g\; \backslash leq\; h$. There exists a continuous function $f\backslash colon\; X\; \backslash to\; \backslash mathbb$ with $g\; \backslash leq\; f\; \backslash leq\; h.$ This theorem has a number of applications and is the first of many classical insertion theorems. In particular it implies the Tietze extension theorem and consequently Urysohn's lemma, and so the conclusion of the theorem is equivalent to normality. ==References== 〔 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「Katětov–Tong insertion 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.