Strong γ-sets and other singular spaces |
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Authors: | Boaz Tsaban |
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Affiliation: | Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot 76100, Israel |
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Abstract: | Whereas the Gerlits-Nagy γ property is strictly weaker than the Galvin-Miller strong γ property, the corresponding strong notions for the Menger, Hurewicz, Rothberger, Gerlits-Nagy (∗), Arkhangel'ski?ˇ and Sakai properties are equivalent to the original ones. The main result is that almost each of these properties admits the game theoretic characterization suggested by the stronger notion. We also solve a related problem of Ko?inac and Scheepers, and answer a question of Iliadis. |
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Keywords: | primary, 37F20 secondary, 26A03, 03E75 |
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