Related papers: Pseudocompact paratopological groups that are topo…

We introduce the concept of a topological J-group and determine for many important examples of topological groups if they are topological J-groups or not. Besides other results, we show that the underlying topological space of a pathwise…

We give the sufficient condition when every left-continuous (right-continuous) Hausdorff topology on a semigroup $S$ is discrete. We construct a submonoid $\mathscr{C}_{+}(a,b)$ (resp., $\mathscr{C}_{-}(a,b)$) of the bicyclic monoid which…

The paper deals with quasigroups having a trivial group of automorphisms and a trivial group of autotopisms. Examples of such quasigroups and methods of their verification are given.

In this work we have considered the complexity of the different structures as topological group on Z. We collect some new results, as well as some known results on the group of the integers in order to present: -A family of $2^\cont$…

We give a complete characterization of the locally compact groups that are non-elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting…

We will consider various definitions of topological entropy for multivalued nonautonomous dynamical systems in compact Hausdorff spaces. Some of them can deal with arbitrary multivalued maps, i.e. when no restrictions are imposed on them.…

A Hausdorff topological group G is minimal if every continuous isomorphism f : G --> H between G and a Hausdorff topological group H is open. Clearly, every compact Hausdorff group is minimal. It is well known that every infinite compact…

A topological group is locally pseudocompact if it contains a non-empty open set with pseudocompact closure. In this note, we prove that if G is a group with the property that every closed subgroup of G is locally pseudocompact, then G_0 is…

In this paper, we firstly construct a Hausdorff non-submetrizable paratopological group $G$ in which every point is a $G_{\delta}$-set, which gives a negative answer to Arhangel'ski\v{\i}\ and Tkachenko's question [Topological Groups and…

We describe the structure of ($0$-)simple inverse Hausdorff semitopological $\omega$-semigroups with compact maximal subgroups. In particular, we show that if $S$ is a simple inverse Hausdorff semitopological $\omega$-semigroup with compact…

Consider a relatively hyperbolic group G. We prove that if G is finitely presented, so are its parabolic subgroups. Moreover, a presentation of the parabolic subgroups can be found algorithmically from a presentation of G, a solution of its…

We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups $G$ such that every element of $G$ is contained in a compact open normal subgroup of $G$. For…

It is shown that a closed solvable subgroup of a connected Lie group is compactly generated. In particular, every discrete solvable subgroup of a connected Lie group is finitely generated. Generalizations to locally compact groups are…

Let $G$ be a finite group and $A$ be a subgroup of $G$. Then $A$ is called a $p$-$CAP$-subgroup of $G$, if $A$ covers or avoids every $pd$-chief factor of $G$. A subgroup $H$ of $G$ is said to be an $ICPC$-subgroup of $G$, if $H \cap [H,G]…

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 $H$…

We define $\Delta$-Baire spaces. If a paratopological group $G$ is $\Delta$-Baire space, then $G$ is a topological group. Locally pseudocompact spaces, Baire $p$-spaces, Baire $\Sigma$-spaces, products of \v{C}ech-complete spaces are…

Let $\mathcal C$ be a subcategory of the category of topologized semigroups and their partial continuous homomorphisms. An object $X$ of the category ${\mathcal C}$ is called ${\mathcal C}$-closed if for each morphism $f:X\to Y$ of the…

We introduce the notion of smooth cell complexes and its subclass consisting of gathered cell complexes within the category of diffeological spaces (cf. Definitions 1 and 3). It is shown that the following hold. (1) With respect to the…

In the paper it is shown that every Hausdorff locally compact semigroup topology on the extended bicyclic semigroup with adjoined zero $\mathscr{C}_{\mathbb{Z}}^{\mathbf{0}}$ is discrete, but on $\mathscr{C}_{\mathbb{Z}}^{\mathbf{0}}$ there…

Let us call a (para)topological group \emph{strongly submetrizable} if it admits a coarser separable metrizable (para)topological group topology. We present a characterization of simply $sm$-factorizable (para)topo\-logical groups by means…