[EN] We show that if a product space $\mathit\Pi$ has countable cellularity, then a dense subspace $X$ of $\mathit\Pi$ is Baire provided that all projections of $X$ to countable subproducts of $\mathit\Pi$ are Baire. It ...
Banak, Taras; Guran, Igor; Ravsky, Alex(Universitat Politècnica de València, 2011-04-01)
[EN] We prove that a Hausdorff paratopological group G is meager if andonly if there are a nowhere dense subset A G and a countable setC G such that CA = G = AC.
Elfard, Ali Sayed(Universitat Politècnica de València, 2015-10-01)
[EN] Let FP(X) be the free paratopological group on a topological space X in the sense of Markov. In this paper, we study the group FP(X) on a $P_\alpha$-space $X$ where $\alpha$ is an infinite cardinal and then we prove ...
Buzyakova, Raushan(Universitat Politècnica de València, 2024-04-02)
[EN] We study topological groups of monotonic automorphisms on a generalized ordered space L. We find a condition that is necessary and sufficient for the set of all monotonic automorphism on L along with the function ...
Fernández, Manuel; Tkachenko, Mikhail G.(Editorial Universitat Politècnica de València, 2014-10-01)
[EN] It is shown that if all countable subgroups of a semitopological group G are precompact, then G is also precompact and that the closure of an arbitrary subgroup of G is again a subgroup. We present a general method ...