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On homeomorphism groups and the compact open topology. (English) Zbl 1135.54023
If every point of a noncompact Hausdorff space \(X\) has a neighbourhood which is a continuum then the compact-open topology on the space of homeomorphisms \(\mathcal H(X)\) coincides with the topology inherited from the topological group of homeomorphisms of the one-point compactification of \(X\). An example is given of a locally compact metric space \(X\) for which the inverse operation on \(\mathcal H(X)\) is not continuous.

54H11 Topological groups (topological aspects)
22A05 Structure of general topological groups
54C35 Function spaces in general topology
58D05 Groups of diffeomorphisms and homeomorphisms as manifolds
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