Embedding of graph inverse semigroups into CLP-compact topological semigroups

TL;DR

This paper characterizes which graph inverse semigroups can be embedded into compact-like topological semigroups, focusing on their topological properties and dense embeddings.

Contribution

It provides a characterization of graph inverse semigroups that admit a compact topology and can be densely embedded into CLP-compact topological semigroups.

Findings

Characterization of graph inverse semigroups with compact semigroup topology

Description of embeddings into CLP-compact topological semigroups

Conditions for dense embeddings of graph inverse semigroups

Abstract

In this paper we investigate graph inverse semigroups which are subsemigroups of compact-like topological semigroups. More precisely, we characterise graph inverse semigroups which admit a compact semigroup topology and describe graph inverse semigroups which can be embeded densely into CLP-compact topological semigroups.