A note on joint metrizability of spaces on families of subspaces. (English) Zbl 1318.54014
Authors’ abstract: “In this note we introduce the concepts of \(JSM\)-spaces and \(JADM\)-spaces following a general idea of Arhangel’skii and Shumrani. Let \(X\) be a topological space. Define \({{F}_{S}}\left( X \right)=\left\{ S\cup \left\{ {{x}_{S}}\right\}:\;S {\text{ is a convergent sequence of }X} which converges to the point \)
Reviewer: Ruzinazar Beshimov (Tashkent)
MSC:
| 54E35 | Metric spaces, metrizability |
| 54A25 | Cardinality properties (cardinal functions and inequalities, discrete subsets) |
| 54B05 | Subspaces in general topology |
Keywords:
compactly metrizable; sequentially compact; strong \(\Sigma^{\ast}\)-space; {JSM}-space; {JADM}-spaceReferences:
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