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Some new versions of an old game

Vladimir Vladimirovich Tkachuk (1995)

Commentationes Mathematicae Universitatis Carolinae

The old game is the point-open one discovered independently by F. Galvin [7] and R. Telgársky [17]. Recall that it is played on a topological space X as follows: at the n -th move the first player picks a point x n X and the second responds with choosing an open U n x n . The game stops after ω moves and the first player wins if { U n : n ω } = X . Otherwise the victory is ascribed to the second player. In this paper we introduce and study the games θ and Ω . In θ the moves are made exactly as in the point-open game, but the...

Some non-multiplicative properties are l -invariant

Vladimir Vladimirovich Tkachuk (1997)

Commentationes Mathematicae Universitatis Carolinae

A cardinal function ϕ (or a property 𝒫 ) is called l -invariant if for any Tychonoff spaces X and Y with C p ( X ) and C p ( Y ) linearly homeomorphic we have ϕ ( X ) = ϕ ( Y ) (or the space X has 𝒫 ( X 𝒫 ) iff Y 𝒫 ). We prove that the hereditary Lindelöf number is l -invariant as well as that there are models of Z F C in which hereditary separability is l -invariant.

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