# Compactness of the automorphism group of a topological parallelism on real projective 3-space

## TL;DR

This paper investigates the automorphism group of topological parallelisms on real projective 3-space, conjecturing its compactness and proving the compactness of its identity component.

## Contribution

It introduces the conjecture that the entire automorphism group is compact and proves the compactness of its identity component.

## Key findings

- The identity component of the automorphism group is compact.
- Supports the conjecture that the entire automorphism group is compact.

## Abstract

We conjecture that the automorphism group of a topological parallelism on real projective 3-space is compact. We prove that at least the identity component of this group is, indeed, compact.