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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 be a normal topological space and let be functions with g upper semicontinuous, h lower semicontinuous and . There exists a continuous function with 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
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