We present a survey on paratopological and semitopological groups relating these classes
with the class of topological groups. A special attention is given to compactness-type …

We prove that a semiregular topological space $ X $ is completely regular if and only if its
topology is generated by a normal quasi-uniformity. This characterization implies that each …

This is a survey on the recent progress in minimal topological groups, with a particular
emphasis on constructions leading to non-abelian minimal groups, as semidirect products …

A topological space X is called a coset space if X is homeomorphic to a quotient space G/H
of left cosets, for some closed subgroup H of a topological group G. In this paper, we …

We prove that for every semitopological group G and every i∈{0, 1, 2, 3, 3.5}, there exists a
continuous homomorphism φ G, i: G→ H onto a T i (resp., T i & T 1 for i⩾ 3) semitopological …

In this paper, we firstly construct a Hausdorff non-submetrizable paratopological group G in
which every point is a Gδ-set, which gives a negative answer to Arhangelʼskiı̌ and …

Groups with a topology that is in consistent one way or another with the algebraic structure
are considered. Well-known classes of groups with a topology are topological …

In this paper, we investigate submetrizability and first-countability of coset spaces. It is
mainly shown that (1) If H is a compact subgroup of a paratopological group G such that l …

We give a characterization of the paratopological groups that can be topologically
embedded as subgroups into a product of first-countable (second-countable) T i …

We show that a regular totally ω-narrow paratopological group G has countable index of
regularity, ie, for every neighborhood U of the identity e of G, we can find a neighborhood V …