On subspaces of measurable real functions.
On Telgársky's question concerning β-favorability of the strong Choquet game
Answering a question of Telgársky in the negative, it is shown that there is a space which is β-favorable in the strong Choquet game, but all of its nonempty -subspaces are of the second category in themselves.
On β-favorability of the strong Choquet game
In the main result, partially answering a question of Telgársky, the following is proven: if X is a first countable R₀-space, then player β (i.e. the EMPTY player) has a winning strategy in the strong Choquet game on X if and only if X contains a nonempty -subspace which is of the first category in itself.
On Baireness of the Wijsman Hyperspace
Baireness of the Wijsman hyperspace topology is characterized for a me- trizable base space with a countable-in-itself p-base; further a separable 1st category metric space is constructed with a Baire Wijsman hyperspace.
Corrigendum to "On Baireness of the Wijsman Hyperspace"
Products of Baire spaces revisited
Generalizing a theorem of Oxtoby, it is shown that an arbitrary product of Baire spaces which are almost locally universally Kuratowski-Ulam (in particular, have countable-in-itself π-bases) is a Baire space. Also, partially answering a question of Fleissner, it is proved that a countable box product of almost locally universally Kuratowski-Ulam Baire spaces is a Baire space.
Baire spaces and weak topologies generated by gap and excess functionals
On a typical property of functions
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