Ahmed Bouziad

Continuity of separately continuous group actions in p-spaces

Let ƒ:X × Y → Z be a separately continuous mapping, where X is a Baire p-space and Z a completely regular space, and let y ϵ Y be a q-point. We show that 1. (i) ƒis strongly quasicontinuous at each point of X × {y}, 2. (ii) if Z is a p-space, then ƒ is subcontinuous at each point of A × {y}, where A is a dense subset of X. Then, we use (i) and (ii) to prove that every separately continuous action of a left topological group, which is a Baire p-space, in a p-space, is a continuous action. In particular, every semitopological group, which is a Baire p-space, has a continuous multiplication.

Borel measures in consonant spaces

Abstract A topology T on a set X is called consonant if the Scott topology of the lattice T is compactly generated; equivalently, if the upper Kuratowski topology and the co-compact topology on closed sets of X coincide. It is proved that every completely regular consonant space is a Prohorov space, and that every first countable regular consonant space is hereditarily Baire. If X is metrizable separable and co-analytic, then X is consonant if and only if X is Polish. Finally, we prove that every pseudocompact topological group which is consonant is compact. Several problems of Dolecki, Greco and Lechicki, of Nogura and Shakmatov, are solved.

The class of co-Namioka compact spaces is stable under product

A Baire space

On hereditary Baireness of the Vietoris topology

B

Filters, consonance and hereditary Baireness

and a compact space

A note on consonance of Gδ subsets

K

Coincidence of the upper Kuratowski topology with the co-compact topology on compact sets, and the Prohorov property

satisfy the Namioka property

Čech-complete spaces and the upper topology

N(B,K)

H-trivial spaces

if for every separately continuous function

Problems about the uniform structures of topological groups

f: B\times K\to R