16 citations · 106 across the 45 of their papers we have counts for
7 papers · 1 filter
Countable tightness and -bases on Free topological groups
Fucai Lin, Alex Ravsky, Jing Zhang
Given a Tychonoff space , let and be respectively the free topological group and the free Abelian topological group over in the sense of Markov. In this paper,…
The closed Steinhaus properties of -ideals on topological groups
Taras Banakh, Lesia Karchevska, Alex Ravsky
We prove that any meager quasi-analytic subgroup of a topological group belongs to every -ideal on possessing the closed -Steinhaus property for some…
Kuratowski monoids of -topological spaces
T. Banakh, O. Chervak, T. Martynyuk +3
Generalizing the famous 14-set closure-complement Theorem of Kuratowski from 1922, we prove that for a set endowed with pairwise comparable topologies $τ_1\subset\dots\subs…
-closed quasitopological groups
Serhiy Bardyla, Oleg Gutik, Alex Ravsky
An -closed quasitopological group is a Hausdorff quasitopological group which is contained in each Hausdorff quasitopological group as a closed subspace. We obtained a sufficien…
Manifolds admitting a continuous cancellative binary operation are orientable
Taras Banakh, Igor Guran, Alex Ravsky
We prove that a topological manifold (possibly with boundary) admitting a continuous cancellative binary operation is orientable. This implies that the Möbius band admits no cancel…
On the submetrizability number and -weight of quasi-uniform spaces and paratopological groups
Taras Banakh, Alex Ravsky
We derive many upper bounds on the submetrizability number and -weight of paratopological groups and topological monoids with open shifts. In particular, we prove that each firs…
Verbal covering properties of topological spaces
Taras Banakh, Alex Ravsky
For any topological space we study the relation between the universal uniformity , the universal quasi-uniformity and the universal pre-uniformity…