Related papers: Pseudocompact and precompact subsemigroups of topo…
The paper is devoted to study the behavior of quasitopological homotopy groups on inverse limit spaces. More precisely, we present some conditions under which the quasitopological homotopy group of an inverse limit space and especially a…
We introduce so-called cone topologies of paratopological groups, which are a wide way to construct counterexamples, especially of examples of compact-like paratopological groups with discontinuous inversion. We found a simple interplay…
We study groups endowed with Alexandroff topologies and show that no non-discrete Alexandroff topology can turn a group into a topological group. This settles negatively the basic existence problem for Alexandroff topological groups.…
We present a general result about generating group topologies by pseudo-norms. Namely, we show that if a topology has a base of sets which are closed in a certain sense, then it can be generated by a collection of pseudo-norms such that the…
For each of the following conditions, we characterize the pseudovarieties of semigroups V that satisfy it: (i) every epimorphism to a member of V is onto; (ii) every epimorphism to a finite semigroup with domain a member of V is onto; (iii)…
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…
A space $X$ is called {\it selectively pseudocompact} if for each sequence $(U_{n})_{n\in \mathbb{N}}$ of pairwise disjoint nonempty open subsets of $X$ there is a sequence $(x_{n})_{n\in \mathbb{N}}$ of points in $X$ such that $cl_X(\{x_n…
A class of almost paratopological groups is introduced, which (1) contains paratopological groups and Hausdorff quasitopological groups; (2) is closed under products; (3) subgroups. Almost paratopological $T_1$ groups $G$ are characterized…
We present a study of semigroup compactifications of a semitopological semigroup $S$ using certain filters on $S$. We characterize closed subsemigroups and closed left, right, and two-sided ideals in any semigroup compactification of any…
We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C(p,q). We prove that each topological semigroup S with pseudocompact square contains no dense copy of C(p,q). On the other…
We introduce two minimality properties of subgroups in topological groups. A subgroup $H$ is a key subgroup (co-key subgroup) of a topological group $G$ if there is no strictly coarser Hausdorff group topology on $G$ which induces on $H$…
Assume that $\mathcal{P}$ is a topological property of a space $X$, then we say that $X$ is {\it dense-$\mathcal{P}$} if each dense subset of $X$ has the property $\mathcal{P}$. In this paper, we mainly discuss dense subsets of a space $X$,…
We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We…
A subgroup of a group is contranormal if its normal closure coincides with the group. We call such groups without proper contranormal subgroups contranormal-free. In this paper we prove various results concerning contranormal-free groups…
In this paper, we show that every topological group is a strong small loop transfer space at the identity element. This implies that the quasitopological fundamental group of a connected locally path connected topological group is a…
We prove that if $H$ is a topological group such that all closed subgroups of $H$ are separable, then the product $G\times H$ has the same property for every separable compact group $G$. Let $c$ be the cardinality of the continuum. Assuming…
We show that all countable subsets of any pseudocompact quasitopological group in the form of a Korovin orbit are closed, discrete, and $C^\ast$-embedded. Consequently, any infinite pseudocompact Korovin orbit is not homeomorphic to a…
A semigroup $T$ is called Taimanov if $T$ contains two distinct elements $0,\infty$ such that $xy=\infty$ for any distinct points $x,y\in T\setminus\{0,\infty\}$ and $xy=0$ in all other cases. We prove that any Taimanov semigroup $T$ has…
A space X is selectively sequentially pseudocompact if for every sequence (U_n) of non-empty open subsets of X, one can choose a point x_n in each U_n in such a way that the sequence (x_n) has a convergent subsequence. Let G be a group from…
For a subgroup of a free product of finite groups, we obtain necessary conditions (on its Kurosh decomposition) to be verbally closed.