The compact-open topology on the homeomorphism group of a surface without boundary is minimal
Geometric Topology
2022-11-08 v3 General Topology
Abstract
We show that the homeomorphism group of a surface without boundary does not admit a Hausdorff group topology strictly coarser than the compact-open topology. In combination with known automatic continuity results, this implies that the compact-open topology is the unique Hausdorff separable group topology on the group if the surface is closed or the complement in a closed surface of either a finite set or the union of a finite set and a Cantor set.
Keywords
Cite
@article{arxiv.2210.17280,
title = {The compact-open topology on the homeomorphism group of a surface without boundary is minimal},
author = {J. de la Nuez González},
journal= {arXiv preprint arXiv:2210.17280},
year = {2022}
}
Comments
15 pages, Lemma 3.6 has been corrected. The argument why K\union L was contained in the closure of U_0 was faulty