Related papers: On topological McAlister semigroups

We study algebraic structure of the $\lambda$-polycyclic monoid $P_{\lambda}$ and its topologizations. We show that the $\lambda$-polycyclic monoid for an infinite cardinal $\lambda\geqslant 2$ has similar algebraic properties so has the…

We present a complete classification of Hausdorff locally compact polycyclic monoids up to a topological isomorphism. A {\em polycyclic monoid} is an inverse monoid with zero, generated by a subset $\Lambda$ such that $xx^{-1}=1$ for any…

In this paper we study the semigroup $\mathscr{I}^{\infty}_\lambda$ of injective partial selfmaps almost everywhere the identity of a set of infinite cardinality $\lambda$. We describe the Green relations on $\mathscr{I}^{\infty}_\lambda$,…

We describe the structure of Hausdorff locally compact semitopological $0$-bisimple inverse $\omega$-semigroups with compact maximal subgroups. In particular, we show that a Hausdorff locally compact semitopological $0$-bisimple inverse…

We prove that a Hausdorff locally compact semitopological bicyclic semigroup with adjoined zero $\mathscr{C}^0$ is either compact or discrete. Also we show that the similar statement holds for a locally compact semitopological bicyclic…

We study topologization of the semigroup $\mathscr{O\!\!I}\!_n(L)$ of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set $(L,\leqslant)$. In particular we show that every $T_1$ left-topological…

We study the semigroup extension $\mathscr{I}_\lambda^n(S)$ of a semigroup $S$ by symmetric inverse semigroups of a bounded finite rank. We describe idempotents and regular elements of the semigroups $\mathscr{I}_\lambda^n(S)$ and…

We study the semigroup $\mathscr{I}^{\mathrm{cf}}_\lambda$ of injective partial cofinite selfmaps of an infinite cardinal $\lambda$. We show that $\mathscr{I}^{\mathrm{cf}}_\lambda$ is a bisimple inverse semigroup and each chain of…

Consider the following generalization of the bicyclic monoid. Let $\kappa$ be any infinite cardinal and let $\mathcal{IP\!F}\left(\sigma{\mathbb{N}^\kappa}\right)$ be the semigroup of all order isomorphisms between principal filters of the…

A result due to M. Gromov states that any two finitely generated groups {\Gamma} and {\Lambda} are quasi-isometric if and only if they admit a topological coupling, i.e., a commuting pair of proper continuous cocompact actions…

We study topological properties of the symmetric inverse topological semigroup of finite transformations $\mathscr{I}_\lambda^n$ of the rank $\leqslant n$. We show that the topological inverse semigroup $\mathscr{I}_\lambda^n$ is…

We show that the topological full group of a Hausdorff ample groupoid with compact unit space coincides with the group of homotopy classes of invertible isometries in pseudofunction algebras associated with the groupoid. Moreover, if the…

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…

In this paper we explore the extent to which the algebraic structure of a monoid $M$ determines the topologies on $M$ that are compatible with its multiplication. Specifically we study the notions of automatic continuity; minimal Hausdorff…

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 $M$ be a manifold and $\Lambda$ a compact exact connected Lagrangian submanifold of $T^*M$. We can associate with $\Lambda$ a conic Lagrangian submanifold $\Lambda'$ of $T^*(M\times R)$. We prove that there exists a canonical sheaf $F$…

The group of automorphisms of the Brandt $\lambda^0$-extension $B^0_\lambda(S)$ of an arbitrary monoid $S$ with zero is described. In particular we show that the group of automorphisms $\mathbf{Aut}(B_{\lambda}^0(S))$ of $B_{\lambda}^0(S)$…

We extend the proof of automatic continuity for homeomorphism groups of manifolds to non-compact manifolds and manifolds with marked points and their mapping class groups. Specifically, we show that, for any manifold $M$ homeomorphic to the…

We call a restriction semigroup almost perfect if it is proper and its least monoid congruence is perfect. We show that any such semigroup is isomorphic to a `$W$-product' $W(T,Y)$, where $T$ is a monoid, $Y$ is a semilattice and there is a…

Let $n$ be any positive integer and $\mathscr{I\!P\!F}(\mathbb{N}^n)$ be the semigroup of all order isomorphisms between principal filters of the $n$-th power of the set of positive integers $\mathbb{N}$ with the product order. We prove…