Hyperspaces of Closed Limit Sets

TL;DR

This paper explores the properties of hyperspaces formed by closed limit sets in a topological space, focusing on Michael's lower semifinite topology and Fell's topology, especially on maximal limit sets.

Contribution

It provides a detailed analysis of the topological structures on collections of closed limit sets, highlighting the behavior of maximal limit sets under these topologies.

Findings

Characterization of Michael's lower semifinite topology on closed limit sets

Analysis of Fell's topology on hyperspaces of limit sets

Insights into the structure of maximal limit sets

Abstract

We study Michael's lower semifinite topology and Fell's topology on the collection of all closed limit subsets of a topological space. Special attention is given to the subfamily of all maximal limit sets.