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.
The compact-open topology on the diffeomorphism or homeomorphism group of a smooth manifold without boundary is minimal in almost all dimensions
Automatic continuity in homeomorphism groups of compact 2-manifolds
A characteristic class of $\mathrm{Homeo(X)_0}$-bundles and an abelian extension of the homeomorphism group
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