Related papers: On semitopological simple inverse $\omega$-semigro…

A Hausdorff topological group $(G,\tau)$ is called an $s$-group and $\tau$ is called an $s$-topology if there is a set $S$ of sequences in $G$ such that $\tau$ is the finest Hausdorff group topology on $G$ in which every sequence of $S$…

A semigroup S containing a zero element is said to be 0-left cancellative if st = sr \neq 0 implies that t = r. Given such an S we build an inverse semigroup H(S), called the inverse hull of S. Motivated by the study of certain C*-algebras…

A Hausdorff topological group G is minimal if every continuous isomorphism f: G --> H between G and a Hausdorff topological group H is open. Significantly strengthening a 1981 result of Stoyanov, we prove the following theorem: For every…

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…

In this paper, we aim to establish a new shape theory, compact Hausdorff shape (CH-shape) for general Hausdorff spaces. We use the "internal" method and direct system approach on the homotopy category of compact Hausdorff spaces. Such a…

Let $H$ be a real algebraic group acting equivariantly with finitely many orbits on a real algebraic manifold $X$ and a real algebraic bundle $\mathcal{E}$ on $X$. Let $\mathfrak{h}$ be the Lie algebra of $H$. Let…

Let $G$ be a group of homeomorphisms of a topological space $X$. $G$ is $\textit{(properly) isometrizable}$ if there exists a $G$-invariant (proper) gauge structure on $X$. $G$ is $\textit{equiregular}$ if for every $x \in X$ and every open…

We extend the classical theory of homotopical $\Sigma$-sets $\Sigma^n$ developed by Bieri, Neumann, Renz and Strebel for abstract groups, to $\Sigma$-sets $\Sigma_{\mathrm{top}}^n$ for locally compact Hausdorff groups. Given such a group…

Let $M$ be a locally symmetric irreducible closed manifold of dimension $\ge 3$. A result of Borel [Bo] combined with Mostow rigidity imply that there exists a finite group $G = G(M)$ such that any finite subgroup of $\text{Homeo}^+(M)$ is…

In the paper we describe the group $\mathbf{Aut}\left(\mathscr{C}_{\mathbb{Z}}\right)$ of automorphisms of the extended bicyclic semigroup $\mathscr{C}_{\mathbb{Z}}$ and study the variants $\mathscr{C}_{\mathbb{Z}}^{m,n}$ of the extended…

We show that the centraliser of the maximal compact subgroup of the real orthogonal or symplectic groups acting on tensors of their standard representation are isomorphic to cyclotomic Brauer algebras. We also show that for the symplectic…

We investigate the algebra of a Hausdorff ample groupoid, introduced by Steinberg, over a commutative semiring S. In particular, we obtain a complete characterization of congruence-simpleness for such Steinberg algebras, extending the…

We show that the homeomorphism group of a surface without boundary does not admit a Hausdorff group topology strictly coarser than the compact-open topology. In combination with known automatic continuity results, this implies that the…

An \emph{affine subtorus} of the compact torus $T=(S^1)^n$ is a translated copy of a Lie subgroup. Given a finite collection $T_1,\ldots, T_k$ of such subtori, and a prime $p$, we describe an explicit chain complex that calculates the group…

In the paper we study the preservation of pseudocompactness (resp., countable compactness, sequential compactness, $\omega$-boundedness, totally countable compactness, countable pracompactness, sequential pseudocompactness) by Tychonoff…

We study the large scale geometry of mapping class groups MCG(S), using hyperbolicity properties of curve complexes. We show that any self quasi-isometry of MCG(S) (outside a few sporadic cases) is a bounded distance away from a…

Recall that a topological space is said to be a $k_\omega$-space if it is the direct limit of an ascending sequence of compact Hausdorff topological spaces. If each point in a Hausdorff space $X$ has an open neighbourhood which is a…

The class, denoted by $\mathscr{S}$, of totally disconnected locally compact groups which are non-discrete, compactly generated, and topologically simple contains many compelling examples. In recent years, a general theory for these groups,…

A topological group G is h-complete if every continuous homomorphic image of G is (Raikov-)complete; we say that G is hereditarily h-complete if every closed subgroup of G is h-complete. In this paper, we establish open-map properties of…

We investigate semigroup topologies on the full transformation monoid T(X) of an infinite set X. We show that the standard pointwise topology is the weakest Hausdorff semigroup topology on T(X), show that the pointwise topology is the…