相关论文: Topological monoids of monotone injective partial …

We construct two non-discrete inverse semigroup $T_1$-topologies and a compact inverse shift-continuous $T_1$-topology on the bicyclic monoid ${\mathscr{C}}(p,q)$. Also we give conditions on a $T_1$-topology $\tau$ on ${\mathscr{C}}(p,q)$…

In this paper we consider a semitopological $\alpha$-bicyclic monoid $\mathcal{B}_{\alpha}$ and prove that it is algebraically isomorphic to a semigroup of all order isomorphisms between the principal upper sets of the ordinal…

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…

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…

Let $\boldsymbol{B}_{[0,\infty)}$ be the semigroup which is defined in the Ahre paper \cite{Ahre=1981}. The semigroup $\boldsymbol{B}_{[0,\infty)}$ with the induced usual topology $\tau_u$ from $\mathbb{R}^2$, with the topology $\tau_L$…

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 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…

For a linearly ordered group $G$ let us define a subset $A\subseteq G$ to be a \emph{shift-set} if for any $x,y,z\in A$ with $y < x$ we get $x\cdot y^{-1}\cdot z\in A$. We describe the natural partial order and solutions of equations on the…

We study congruences of the semigroup $\mathscr{I\!O}\!_{\infty}(\mathbb{Z}^n_{\operatorname{lex}})$ of monotone injective partial selfmaps of the set of $L_n\times_{\operatorname{lex}}\mathbb{Z}$ having co-finite domain and image, where…

We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locally compact and $\sigma$-compact group $\Gamma$ is…

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…

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…

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…

Totally positive (TP) and totally nonnegative (TN) matrices connect to analysis, mechanics, and to dual canonical bases in reductive groups, by well-known works of Schoenberg, Gantmacher-Krein, Lusztig, and others. TP matrices form a…

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…

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…

We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse…

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 introduce the inverse monoid of inner partial automorphisms of a semigroup -- a tool that associates to every semigroup an inverse semigroup. When the semigroup is a group, this inverse semigroup is isomorphic to the group of inner…