Some methods for generating topologies by relations.
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 as follows: at the -th move the first player picks a point and the second responds with choosing an open . The game stops after moves and the first player wins if . Otherwise the victory is ascribed to the second player. In this paper we introduce and study the games and . In the moves are made exactly as in the point-open game, but the...
A cardinal function (or a property ) is called -invariant if for any Tychonoff spaces and with and linearly homeomorphic we have (or the space has () iff ). We prove that the hereditary Lindelöf number is -invariant as well as that there are models of in which hereditary separability is -invariant.