On two selection principles and the corresponding games (Q386844)
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scientific article; zbMATH DE number 6237315
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On two selection principles and the corresponding games |
scientific article; zbMATH DE number 6237315 |
Statements
On two selection principles and the corresponding games (English)
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11 December 2013
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selection principles
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topological games
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dense open families
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Pixley-Roy hyperspace
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winning strategy
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A family \(\mathbf U\) of subsets of a topological space is dense if the union of the members of \(\mathbf U\) is a dense subset. The symbols \(\mathbf D_0\) and \(\mathbf D\) denote respectively the collection of all dense open families and the collection of all dense subsets.NEWLINENEWLINEIn this paper the author studies extensively the selection principles \(S_1(\mathbf D_0,\mathbf D_0)\) and \(S_{\text{fin}}(\mathbf D_0,\mathbf D_0)\) and the corresponding topological games. The Pixley-Roy topology plays a major role in this investigation. Several interesting results are obtained and some open questions for further consideration are posed.
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