Add to ORKGIt is shown that a metrizable space X, with completely metrizable separable closed subspaces, has a hereditarily Baire hyperspace K(X) of nonempty compact subsets of X endowed with the Vietoris topology tv. In particular, making use of a construction of Saint Raymond, we show in ZFC that there exists a non-completely metrizable, metrizable space X with hereditarily Baire hyperspace (K(X),tv); thus settling a problem of Bouziad. Hereditary Baireness of (K(X),tv) for a Moore space X is also characterized in terms of an auxiliary product space and the strong Choquet game. Finally, using a result of Kunen, a non-consonant metrizable space having completely metrizable separable closed subspaces is constructed under CH. ? 2001 Elsevier Science B....
AbstractVery recently Tkachuk has proved that for a completely regular Hausdorff space X the space C...
It is well-known, that if X ×Y is a Baire space, then X, Y are Baire as well, and the converse is no...
The family of sets with the Baire property of a topological space X, i.e., sets which differ from op...
AbstractIt is shown that a metrizable space X, with completely metrizable separable closed subspaces...
International audienceIt is shown that a metrizable space X, with completely metrizable separable cl...
We prove that if the Vietoris hyperspace CL(X) of all nonempty closed subsets of a space X is Baire,...
In the past ten years, there has been a great progress in determining when hyperspaces have the Bair...
In this paper, we show that if the Tychonoff power Xω of a quasiregular space X is Baire, then its Vi...
AbstractA Hausdorff space each subspace of which is a paracompact p-space is an Fpp-space. A space X...
Let (K, d) be a separable Baire metric space or a completely metrizable space. It is shown that the ...
AbstractThe space PK of partial maps with compact domains (identified with their graphs) forms a sub...
The space PK of partial maps with compact domains (identified with their graphs) forms a subspace of...
AbstractLet X be a Hausdorff topological space and exp(X) be the space of all (nonempty) closed subs...
New results on the Baire product problem are presented. It is shown that an arbitrary product of alm...
Baireness of the Wijsman hyperspace topology is characterized for a metrizable base space with a cou...
AbstractVery recently Tkachuk has proved that for a completely regular Hausdorff space X the space C...
It is well-known, that if X ×Y is a Baire space, then X, Y are Baire as well, and the converse is no...
The family of sets with the Baire property of a topological space X, i.e., sets which differ from op...
AbstractIt is shown that a metrizable space X, with completely metrizable separable closed subspaces...
International audienceIt is shown that a metrizable space X, with completely metrizable separable cl...
We prove that if the Vietoris hyperspace CL(X) of all nonempty closed subsets of a space X is Baire,...
In the past ten years, there has been a great progress in determining when hyperspaces have the Bair...
In this paper, we show that if the Tychonoff power Xω of a quasiregular space X is Baire, then its Vi...
AbstractA Hausdorff space each subspace of which is a paracompact p-space is an Fpp-space. A space X...
Let (K, d) be a separable Baire metric space or a completely metrizable space. It is shown that the ...
AbstractThe space PK of partial maps with compact domains (identified with their graphs) forms a sub...
The space PK of partial maps with compact domains (identified with their graphs) forms a subspace of...
AbstractLet X be a Hausdorff topological space and exp(X) be the space of all (nonempty) closed subs...
New results on the Baire product problem are presented. It is shown that an arbitrary product of alm...
Baireness of the Wijsman hyperspace topology is characterized for a metrizable base space with a cou...
AbstractVery recently Tkachuk has proved that for a completely regular Hausdorff space X the space C...
It is well-known, that if X ×Y is a Baire space, then X, Y are Baire as well, and the converse is no...
The family of sets with the Baire property of a topological space X, i.e., sets which differ from op...