The \(\sup =\max \) problem for the extent of generalized metric spaces. (Q2856930)
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scientific article; zbMATH DE number 6221266
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The \(\sup =\max \) problem for the extent of generalized metric spaces. |
scientific article; zbMATH DE number 6221266 |
Statements
30 October 2013
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extent
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Lindelöf degree
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\(\Sigma \)-space
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strict \(p\)-space
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semi-stratifiable
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The \(\sup =\max \) problem for the extent of generalized metric spaces. (English)
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The authors consider the \(\sup = \max \) problem for the extent of some classes of generalized metric spaces in the following form: if \(X\) is a generalized metric space with \(e(X) = \kappa \), where \(\kappa \) is a cardinal such that \(cf(\kappa ) > \omega \), is there a closed discrete subset of \(X\) of size \(\kappa \)? By using a new type of the \(\sup = \max \) problem for the Lindelöf degree they prove that the answer to this question is positive for \(\Sigma \)-spaces, strict \(p\)-spaces, paracompact semi-stratifiable spaces. A similar question is discussed for subspaces of cardinals. Three open problems are posed.
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