The compact-open topology on the homeomorphism group of a surface without boundary is minimal

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.

arXiv comment15 pages, Lemma 3.6 has been corrected. The argument why K\union L was contained in the closure of U_0 was faulty