arXiv subjects

Andriy Reiter

Publications and source records attributed to Andriy Reiter.

2 recordsLinked to original sources

arXiv2009

Topological semigroups of matrix units and countably compact Brandt $λ^0$-extensions of topological semigroups

We show that a topological semigroup of finite partial bijections $\mathscr{I}_λ^n$ of an infinite set with a compact subsemigroup of idempotents is absolutely $H$-closed and any countably compact topological semigroup does not contain $\mathscr{I}_λ^n$ as a subsemigroup. We give sufficient conditions onto a topological semigroup $\mathscr{I}_λ^1$ to be non-$H$-closed. Also we describe the structure of countably compact Brandt $λ^0$-extensions of topological monoids and study the category of countably compact Brandt $λ^0$-extensions of topological monoids with zero.

math.GR↗

arXiv2009

Symmetric inverse topological semigroups of finite rank $\leqslant n$

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 algebraically $h$-closed in the class of topological inverse semigroups. Also we prove that a topological semigroup $S$ with countably compact square $S\times S$ does not contain the semigroup $\mathscr{I}_\lambda^n$ for infinite cardinal $\lambda$ and show that the Bohr compactification of an infinite topological symmetric inverse semigroup of finite transformations $\mathscr{I}_\lambda^n$ of the rank $\leqslant n$ is the trivial semigroup.

math.GR↗