Brandt extensions and primitive topological inverse semigroups

TL;DR

This paper investigates the structure and embedding properties of countably compact and H-closed primitive topological inverse semigroups, providing structural descriptions and embedding results for these algebraic-topological objects.

Contribution

It offers a detailed structural description of primitive topological inverse semigroups and proves that any countably compact primitive topological inverse semigroup can be embedded into a compact one.

Findings

Structural description of primitive topological inverse semigroups

Embedding of countably compact into compact primitive inverse semigroups

Characterization of H-closed primitive topological inverse semigroups

Abstract

In the paper we study (countably) compact and (absolutely) $H$-closed primitive topological inverse semigroups. We describe the structure of compact and countably compact primitive topological inverse semigroups and show that any countably compact primitive topological inverse semigroup embeds into a compact primitive topological inverse semigroup.