Some remarks on a game of Telgársky |
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Authors: | P Szewczak |
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Institution: | Faculty of Mathematics and Natural Sciences, College of Sciences, Cardinal Stefan Wyszyński University, Warsaw, Poland |
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Abstract: | In 3] R. Telgársky (1975) asked: does the first player have a winning strategy in the game G(F,X×X) if the first player has a winning strategy in the game G(F,X)? I give a positive answer to this question and prove that this result is also true for spaces where the first player has a winning strategy in game G(K,X) where K=1, F, C, for σC if X is P-space and for DC if X is collectionwise-normal space. The last result is related to the Telgársky's (1983) conjecture discussed in 1]. These results are not true for infinite product of spaces. |
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Keywords: | Telgá rsky's game Paracompact space |
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