A singular space related to the point-open game

Junnila, H. J. K.; Nogura, T.; Telgársky, R.

doi:10.1090/S0002-9939-1987-0875399-6

A singular space related to the point-open game
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by H. J. K. Junnila, T. Nogura and R. Telgársky PDF

Proc. Amer. Math. Soc. 99 (1987), 568-570 Request permission

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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