Pseudocompact primitive topological inverse semigroups

TL;DR

This paper investigates the structure and properties of pseudocompact primitive topological inverse semigroups, demonstrating their structural description, product behavior, and the nature of their Stone-ech compactifications.

Contribution

It provides a detailed structural description and new results on the product and compactification properties of pseudocompact primitive topological inverse semigroups.

Findings

Tychonoff product of pseudocompact primitive topological inverse semigroups is pseudocompact.

Stone-ech compactification of such semigroups is a compact primitive topological inverse semigroup.

The paper characterizes the structure of pseudocompact primitive topological inverse semigroups.

Abstract

In the paper we study pseudocompact primitive topological inverse semigroups. We describe the structure of pseudocompact primitive topological inverse semigroups and show that a Tychonoff product of a family of pseudocompact primitive topological inverse semigroups is a pseudocompact topological space. Also we prove that the Stone-\v{C}ech compactification of a pseudocompact primitive topological inverse semigroup is a compact primitive topological inverse semigroup.