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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A singular space related to the point-open game


Authors: H. J. K. Junnila, T. Nogura and R. Telgársky
Journal: Proc. Amer. Math. Soc. 99 (1987), 568-570
MSC: Primary 54D20; Secondary 54D30, 54G20, 90D99
MathSciNet review: 875399
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Abstract: The authors construct a completely regular space $ {X_0}$ such that Player I has a winning strategy in the point-open game $ G\left( {{X_0}} \right)$, but $ {X_0}$ has no $ \sigma $-closure-preserving cover by $ {\mathbf{C}}$-scattered closed sets.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0875399-6
PII: S 0002-9939(1987)0875399-6
Keywords: Point-open game, compact-like space, closure-preserving, $ \sigma $-closure-preserving, $ {\mathbf{C}}$-scattered, metacompact
Article copyright: © Copyright 1987 American Mathematical Society