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New proofs of classical insertion theorems. (English) Zbl 1038.54007
It is shown that Dowker’s strict insertion theorem for normal countably paracompact spaces follows easily from the Katětov and Tong insertion theorem for normal spaces and Dowker’s result that \(X\times [0,1]\) is normal if (and only if) \(X\) is normal and countably paracompact.
Michael’s insertion theorem for perfectly normal spaces \(X\) is deduced similarly from the Katětov and Tong theorem and from Katětov’s result that \(X\times [0,1]\) is hereditarily normal in this case.
A proof of the Katětov and Tong theorem is given by a modification of Mandelkern’s proof of the Tietze-Urysohn theorem.

MSC:
54C30 Real-valued functions in general topology
54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
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