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Some notes on weakly Whyburn spaces. (English) Zbl 1017.54001
Topology Appl. 128, No. 2-3, 257-262 (2003); corrigendum 138, No. 1-3, 323-324 (2004).
A space \(X\) is weakly Whyburn provided that for each non-closed \(A\subset X\) there is \(x\in\overline A-A\) and \(F\subset A\) with \(\overline F-F=\{ x\}\). Open and closed subsets of weakly Whyburn spaces are also weakly Whyburn but examples are constructed of compact spaces which are weakly Whyburn but have subspaces which are not. Some examples of spaces which are not weakly Whyburn are given, for example \(C_p(\omega_1)\).
Editorial remark on the corrigendum: The author gave an example of a Hausdorff compact sequential space and incorrectly claimed that it was not hereditarily weakly Whyburn. In the corrigendum a correct example of a Hausdorff (scattered) sequential space is presented which is not hereditarily weakly Whyburn. The question about the existence of a Tikhonov (or just regular) sequential space that is not weakly Whyburn remains open

54A05 Topological spaces and generalizations (closure spaces, etc.)
54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
54D55 Sequential spaces
54B05 Subspaces in general topology
Full Text: DOI
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