On Topological Groups of Automorphisms

TL;DR

This paper investigates conditions under which the space of automorphisms of a topological space forms a topological group when equipped with the pointwise convergence topology, identifying classes of spaces with this property.

Contribution

The paper characterizes large classes of spaces where the automorphism space is or isn't a topological group, advancing understanding of automorphism groups in topology.

Findings

Identifies classes of spaces with automorphism groups that are topological groups.

Provides criteria for when the automorphism space fails to be a topological group.

Enhances understanding of the structure of automorphism groups in topology.

Abstract

We study spaces $X$ for which the space $Hom_p(X)$ of automorphisms with the topology of point-wise convergence is a topological group. We identify large classes of spaces $X$ for which $Hom_p(X)$ is or is not a topological group.