On quasitopological homotopy groups of Inverse Limit Spaces

TL;DR

This paper investigates the properties of quasitopological homotopy groups in inverse limit spaces, identifying conditions for them to be topological groups and discussing their countability.

Contribution

It provides new conditions under which quasitopological homotopy groups become topological groups in inverse limit spaces.

Findings

Conditions for quasitopological homotopy groups to be topological groups

Criteria for countability of homotopy groups

Analysis of inverse limit and product spaces

Abstract

The paper is devoted to study the behavior of quasitopological homotopy groups on inverse limit spaces. More precisely, we present some conditions under which the quasitopological homotopy group of an inverse limit space and especially a product space is a topological group. Finally, we give some conditions for countability of homotopy groups.