Compactness of the automorphism group of a topological parallelism on real projective 3-space: The disconnected case

TL;DR

This paper proves that the automorphism group of a topological parallelism on real projective 3-space is compact, extending previous results by removing the assumption about the connected component of the identity.

Contribution

It establishes the compactness of the entire automorphism group without relying on earlier connected component results.

Findings

Automorphism group of topological parallelism is compact

Previous results on connected component are extended

Proof does not depend on earlier connected component assumptions

Abstract

We prove that the automorphism group of a topological parallelism on real projective 3-space is compact. In a preceding article it was proved that at least the connected component of the identity is compact. The present proof does not depend on that earlier result.