Uniqueness results for homeomorphism groups

Kallman, Robert R.

doi:10.1090/S0002-9947-1986-0831205-0

Uniqueness results for homeomorphism groups
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Trans. Amer. Math. Soc. 295 (1986), 389-396 Request permission

Abstract:

Let $X$ be a separable metric manifold and let $\mathcal {H}(X)$ be the homeomorphism group of $X$. Then $\mathcal {H}(X)$ has a unique topology in which it is a complete separable metric group. Similar results are demonstrated for a much wider class of spaces, $X$, and for many subgroups of the homeomorphism group.

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