On compact topologies on the semigroup of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set

Abstract

We study topologization of the semigroup $\mathcal{O}\mathcal{I}{}_n(L)$ of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set $(L,⩽)$. In particular we show that every $T_1$ left-topological (right-topological) semigroup $\mathcal{O}\mathcal{I}{}_n(L)$ is a completely Hausdorff, Urysohn, totally separated, scattered space. We prove that on the semigroup $\mathcal{O}\mathcal{I}{}_n(L)$ admits a unique Hausdorff countably compact (pseudocompact) shift-continuous topology which is compact, and the Bohr compactification of a Hausdorff topological semigroup $\mathcal{O}\mathcal{I}{}_n(L)$ is the trivial semigroup.

9 pages (in Ukrainian)

References in corpus (2)

• Semigroup Closures of Finite Rank Symmetric Inverse Semigroups
• The semigroup of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set