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Non locally compact points in ultracomplete topological spaces. (English) Zbl 0976.54025

Summary: We answer a problem posed by V. I. Ponomarev and V. V. Tkachuk [Mosc. Univ. Math. Bull. 42, No. 5, 14-17 (1987); translation from Vestn. Mosk. Univ., Ser. I 1987, No. 5, 16-19 (1987; Zbl 0637.54003)] related with the subspace \(X_C\) of an ultracomplete space \(X\) consisting of the points in \(X\) admitting no compact neighborhood.

MSC:

54D99 Fairly general properties of topological spaces
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54D45 Local compactness, \(\sigma\)-compactness
54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
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