Reccurence Sets for Partial Inverse, Semigroup Actions and Related Structures

TL;DR

This paper introduces recurrence sets for inverse semigroup partial actions, exploring their connections with similar concepts in related symmetry structures, advancing understanding of imperfect symmetries in topological spaces.

Contribution

It defines new recurrence sets for inverse semigroup partial actions and investigates their relationships with related symmetry notions, providing a novel framework for analyzing imperfect symmetries.

Findings

Recurrence sets are characterized for inverse semigroup partial actions.

Connections are established between recurrence sets and similar notions in prefix inverse semigroup expansions, partial groups, and groupoids.

The framework enhances understanding of imperfect symmetries in topological spaces.

Abstract

Two types of recurrence sets are introduced for inverse semigroup partial actions in topological spaces. We explore their connections with similar notions for related types of imperfect symmetries (prefix inverse semigroup expansions, partial group and groupoid actions).