TY - JOUR

T1 - Some remarks on a game of Telgársky

AU - Szewczak, P.

PY - 2011/2/1

Y1 - 2011/2/1

N2 - 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.

AB - 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.

KW - Paracompact space

KW - Telgársky's game

UR - http://www.scopus.com/inward/record.url?scp=78649631147&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2010.10.011

DO - 10.1016/j.topol.2010.10.011

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AN - SCOPUS:78649631147

SN - 0166-8641

VL - 158

SP - 177

EP - 182

JO - Topology and its Applications

JF - Topology and its Applications

IS - 2

ER -