Related papers: A Note on Locally Compact Subsemigroups of Compact…

We introduce the notion of soficity for locally compact groups and list a number of open problems.

The aim of this paper is to introduce and give preliminary investigation of T-locally compact spaces. Locally compact and T-locally compact are independent of each other. Every Hausdorff, locally compact space is T-locally compact.…

The notion of an open quantum subgroup of a locally compact quantum group is introduced and given several equivalent characterizations in terms of group-like projections, inclusions of quantum group C*-algebras and properties of respective…

In this paper we introduce perfectly supportable semigroups and prove that they are \sigma-discrete in each Hausdorff shift-invariant topology. The class of perfectly supportable semigroups includes each subsemigroup S of the semigroup…

In this paper, we present a simple proof of the fact that any compact subgroup of homeomorphisms of the 2-sphere is topologically conjugate to a closed subgroup of the orthogonal group O(3).

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…

We identify the class of elementary groups: the smallest class of totally disconnected locally compact second countable (t.d.l.c.s.c.) groups that contains the profinite groups and the discrete groups, is closed under group extensions of…

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…

A locally compact contraction group is a pair (G,f) where G is a locally compact group and f an automorphism of G which is contractive in the sense that the forward orbit under f of each g in G converges to the neutral element e, as n tends…

Hrushovski proved the Lie model theorem in full generality with model theoretic methods. The theorem states that for every approximate group there exists a generalized definable locally compact model, which, simplifying, is a…

We show that every Hausdorff Baire topology $\tau$ on $\mathcal{C}=\langle a,b\mid a^2b=a, ab^2=b\rangle$ such that $(\mathcal{C},\tau)$ is a semitopological semigroup is discrete and we construct a nondiscrete Hausdorff semigroup topology…

The aim of this paper is to study the topological properties of some classes of subsemimodules endowed with a subbasis closed-set topology. We show that such spaces are $T_0$. When the semimodule is finitely generated, those spaces are…

We detect topological semigroups that are topological paragroups, i.e., are isomorphic to a Rees product of a topological group over topological spaces with a continuous sandwich function. We prove that a simple topological semigroup $S$ is…

We construct locally compact groups with no non-trivial Invariant Random Subgroups and no non-trivial Uniformly Recurrent Subgroups.

Let $\mathcal C$ be a class of Hausdorff topological semigroups which contains all zero-dimensional Hausdorff topological semigroups. A semigroup $X$ is called $\mathcal C$-$closed$ if $X$ is closed in each topological semigroup $Y\in…

A Hausdorff topological semiring is called simple if every non-zero continuous homomorphism into another Hausdorff topological semiring is injective. Classical work by Anzai and Kaplansky implies that any simple compact ring is finite. We…

We present a contribution to the structure theory of locally compact groups. The emphasis is on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic…

Semigroups generated by topological operations such as closure, interior or boundary are considered. It is noted that some of these semigroups are in general finite and noncommutative. The problem is formulated whether they are always…

We show that for a minimal, second countable, locally compact Hausdorff \'etale groupoid whose unit space is homeomorphic to the Cantor set, if the groupoid has comparison then the commutator subgroup of its full group is simple. This…

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…