Hyperconvergence in topological dynamics

TL;DR

This paper explores hyperconvergence and continuity of orbital and limit set functions in semigroup actions on regular spaces, revisiting hyperspace concepts and examining hyperconvergence types.

Contribution

It provides new insights into hyperconvergence and continuity properties in the context of semigroup actions on topological spaces.

Findings

Analysis of Hausdorff and Kuratowski hyperconvergence

Results on hyperconvergence of orbital and limit set functions

General facts on hyperspace concepts

Abstract

In this manuscript the concept of hyperspace is revisited. The main purpose is to study hyperconvergence and continuity of orbital and limit set functions for semigroup action on completely regular space. Some general facts on Hausdorff and Kuratowski hyperconvergence are presented.