Related papers: A note on compact-like semitopological groups

In this paper, we consider the continuity of the inverse in (strongly) paratopological gyrogroups. The conclusions are established as follows: (1) A compact Hausdorff paratopological gyrogroup $G$ is a topological gyrogroup. (2) A Hausdorff…

The main objects of study in this article are pairs $(G, \mathcal{H})$ where $G$ is a topological group with a compact open subgroup, and $\mathcal{H}$ is a finite collection of open subgroups. We develop geometric techniques to study the…

In this paper we study the separately continuous actions of semitopological monoids on pseudocompact spaces. The main aim of this paper is to generalize Lawson's results to some class of pseudocompact spaces. Also, we introduce a concept of…

We study algebraic and topological properties of subsemigroups of the hyperspace exp(G) of non-empty compact subsets of a topological group G endowed with the Vietoris topology and the natural semigroup operation. On this base we prove that…

We introduce and study oscillator topologies on paratopological groups and define certain related number invariants. As an application we prove that a Hausdorff paratopological group $G$ admits a weaker Hausdorff group topology provided $G$…

In this paper, we pose the concepts of pre-topological groups and some generalizations of pre-topological groups. First, we systematically investigate some basic properties of pre-topological groups; in particular, we prove that each…

Let $H$ be a closed subgroup of a regular abelian paratopological group $G$. The group reflexion $G^\flat$ of $G$ is the group $G$ endowed with the strongest group topology, weaker that the original topology of $G$. We show that the…

We study the closures of subgroups, semilattices and different kinds of semigroup extensions in semitopological inverse semigroups with continuous inversion. In particularly we show that a topological group $G$ is $H$-closed in the class of…

We study the structure of inverse primitive feebly compact semitopological and topological semigroups. We find conditions when the maximal subgroup of an inverse primitive feebly compact semitopological semigroup $S$ is a closed subset of…

An action of a group $G$ on a compact space $X$ is called weakly almost periodic if the orbit of every continuous function on $X$ is weakly relatively compact in $C(X)$. We observe that for a topological group $G$ the following are…

Inspired by an analogous result of Arnautov about isomorphisms, we prove that all continuous surjective homomorphisms of topological groups f:G-->H can be obtained as restrictions of open continuous surjective homomorphisms f':G'-->H, where…

Groups with a topology that is in consistent one way or another with the algebraic structure are considered. Classical groups with a topology are topological, paratopological, semitopological, and quasitopological groups. We also study…

An $H$-closed quasitopological group is a Hausdorff quasitopological group which is contained in each Hausdorff quasitopological group as a closed subspace. We obtained a sufficient condition for a quasitopological group to be $H$-closed,…

An action of a topological semigroup S on X is compactifiable if this action is a restriction of a jointly continuous action of S on a Hausdorff compact space Y. A topological semigroup S is compactifiable if the left action of S on itself…

We endow a topological group $(G, \tau)$ with a coarse structure defined by the smallest group ideal $S_{\tau} $ on $G$ containing all converging sequences with their limits and denote the obtained coarse group by $(G, S_{\tau})$. If $G$ is…

We investigate closed subsets (subsemigroups, resp.) of compact-like topological spaces (semigroups, resp.). We prove that each Hausdorff topological space can be embedded as a closed subspace into an H-closed topological space. However,…

To every directed graph $E$ one can associate a \emph{graph inverse semigroup} $G(E)$, where elements roughly correspond to possible paths in $E$. These semigroups generalize polycylic monoids, and they arise in the study of Leavitt path…

Let $G$ be a locally compact topological group, $G_0$ the connected component of its identity element, and comp(G) the union of all compact subgroups. A topological group will be called inductively monothetic if any subgroup generated (as a…

We introduce a notion of topological entropy for continuous actions of compactly generated topological groups on compact Hausdorff spaces. It is shown that any continuous action of a compactly generated topological group on a compact…

We develop a theory of type semigroups for arbitrary twisted, not necessarily Hausdorff \'etale groupoids. The type semigroup is a dynamical version of the Cuntz semigroup. We relate it to traces, ideals, pure infiniteness, and stable…