On the dichotomy of a locally compact semitopological monoid of order isomorphisms between principal filters of $\mathbb{N}^n$ with adjoined zero

On the dichotomy of a locally compact semitopological bicyclic monoid with adjoined zero

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 semigroup with an adjoined compact ideal and construct an example which witnesses that a counterpart of the statements does not hold when $\mathscr{C}^0$ is a Čech-complete metrizable topological inverse semigroup.

On a semitopological extended bicyclic semigroup with adjoined zero

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 exist $\mathfrak{c}$ many different Hausdorff locally compact shift-continuous topologies. Also, it is constructed on $\mathscr{C}_{\mathbb{Z}}^{\mathbf{0}}$ the unique minimal shift continuous topology and the unique minimal inverse semigroup topology.

On locally compact semitopological $0$-bisimple inverse $ω$-semigroups

We describe the structure of Hausdorff locally compact semitopological $0$-bisimple inverse $ω$-semigroups with compact maximal subgroups. In particular, we show that a Hausdorff locally compact semitopological $0$-bisimple inverse $ω$-semigroup with a compact maximal subgroup is either compact or topologically isomorphic to the topological sum of its $\mathscr{H}$-classes. We describe the structure of Hausdorff locally compact semitopological $0$-bisimple inverse $ω$-semigroups with a monothetic maximal subgroups. In particular we prove the dichotomy for $T_1$ locally compact semitopological …

具有紧极大子群的半拓扑单逆ω-半群研究

On semitopological simple inverse $ω$-semigroups with compact maximal subgroups

该研究刻画了带紧极大子群的单逆Hausdorff半拓扑ω-半群的拓扑结构，证明其拓扑同构于紧群有限半格的Bruck--Reilly扩张，并给出了带零元时这类半群上Hausdorff局部紧移位连续拓扑的两种分类情形。

关于带有一个邻接紧理想的半群 $\boldsymbol{B}_{[0,\infty)}$ 上的局部紧移位连续拓扑

On locally compact shift continuous topologies on the semigroup $\boldsymbol{B}_{[0,\infty)}$ with an adjoined compact ideal

本文研究半群 $\boldsymbol{B}_{[0,\infty)}$ 在三种拓扑下邻接紧理想时的局部紧移位连续拓扑结构，证明理想要么为开子集，要么使半群成为紧半群。

On locally compact semitopological graph inverse semigroups

In this paper we investigate locally compact semitopological graph inverse semigroups. Our main result is the following: if a directed graph $E$ is strongly connected and contains a finite amount of vertices then a locally compact semitopological graph inverse semigroup $G(E)$ is either compact or discrete. This result generalizes results of Gutik and Bardyla who proved the above dichotomy for locally compact semitopological polycyclic monoids $\mathcal{P}_1$ and $\mathcal{P}_λ$, respectively.