Mizokami and Lin's conjecture on \(\sigma -CF^{*}\) pseudo-bases (Q1041657)
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scientific article; zbMATH DE number 5641755
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Mizokami and Lin's conjecture on \(\sigma -CF^{*}\) pseudo-bases |
scientific article; zbMATH DE number 5641755 |
Statements
Mizokami and Lin's conjecture on \(\sigma -CF^{*}\) pseudo-bases (English)
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3 December 2009
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In the paper [Math. Jap. 46, No.~3, 377--384 (1997; Zbl 0992.46008)], \textit{T. Mizokami} and \textit{S. Lin} gave a conjecture on \(\sigma\)-\(CF^*\) pseudo-bases, namely, that every regular space \(X\) with a \(\sigma\)-\(CF^*\) pseudo-base is either an \(\aleph_0\)-space or all compact subsets of \(X\) are finite. The author gives a positive answer to this. Besides, he solves other questions from the book [Open Problems in Topology. II. Amsterdam: Elsevier (2007; Zbl 1158.54300), pp. 731--736].
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\(CF^*\) family
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\(CF\) family
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pseudo-base
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quasi-base
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\(\aleph_0\)-space
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