×

zbMATH — the first resource for mathematics

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

MSC:
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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bella, A., On spaces with the property of weak approximation by points, Comment. math. univ. carolin., 35, 2, 357-360, (1994) · Zbl 0808.54007
[2] Bella, A., Few remarks and questions on pseudoradial and related spaces, Topology appl., 70, 113-123, (1996) · Zbl 0862.54022
[3] Bella, A.; Yashenko, I.V., On whyburn and weakly whyburn spaces, Comment. math. univ. carolin., 40, 3, 531-536, (1999) · Zbl 1010.54040
[4] Gerlits, J.; Nagy, Z.; Szentmiklòssy, Z., Some convergence properties in function spaces, (), 211-222
[5] J. Pelant, M.G. Tkachenko, V.V. Tkachuk, R.G. Wilson, Pseudocompact Whyburn spaces need not be Fréchet, PAMS, to appear · Zbl 1028.54004
[6] Pultr, A.; Tozzi, A., Equationally closed subframes and representation of quotient spaces, Cahiers topologie Géom. différentielle categoriques, 34, 167-183, (1993) · Zbl 0789.54008
[7] Simon, P., On accumulation points, Cahiers topologie Géom. différentielle categoriques, 35, 321-327, (1994) · Zbl 0858.54008
[8] Tkachuk, V.V.; Yashenko, I.V., Almost closed sets and topologies they determine, Comment. math. univ. carolin., 42, 2, 395-405, (2001) · Zbl 1053.54004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.