On continuous isomorphisms from $\sigma$-compact paratopological groups onto topological groups
General Topology
2026-05-29 v1
Abstract
In this short note we give a negative answer to the following open question: \emph{Let be a -compact paratopological group. Does there exist a continuous isomorphism of onto a topological group ?} Specifically, we construct a family of -compact paratopological groups for which a continuous isomorphism onto a topological group exists if and only if carries the trivial topology.
Keywords
Cite
@article{arxiv.2605.29347,
title = {On continuous isomorphisms from $\sigma$-compact paratopological groups onto topological groups},
author = {Pedro J. Chocano and Tayomara Borsich},
journal= {arXiv preprint arXiv:2605.29347},
year = {2026}
}