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

J. de la Nuez González

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arXiv · 2210.17280

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

J. de la Nuez González

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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.

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J. de la Nuez González. 2022-10-31. The compact-open topology on the homeomorphism group of a surface without boundary is minimal. https://arxiv.org/abs/2210.17280

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