A theorem of insertion and extension of functions for normal spaces (Q689765)
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scientific article; zbMATH DE number 446358
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A theorem of insertion and extension of functions for normal spaces |
scientific article; zbMATH DE number 446358 |
Statements
A theorem of insertion and extension of functions for normal spaces (English)
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15 November 1993
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The main result of this paper is a theorem which characterizes the normal spaces as those topological spaces in which it is possible to insert a continuous function \(h\) between two functions \(g\leq f\), being \(g\) upper semicontinuous, \(f\) lower semicontinuous and \(f\) continuous in the closed subset \(C\), with \(h(x)=f(x)\) for every\(x\in C\). The Katětov-Tong theorem and the Tietze-Urysohn theorem are immediate corollaries of this result.
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\({\mathcal C}\)-binary relation
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insertion
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normal space
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semicontinuous function
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Katětov-Tong theorem
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Tietze-Urysohn theorem
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