The closure of the space of homeomorphisms on a manifold

Haver, William E.

doi:10.1090/S0002-9947-1974-0362375-0

The closure of the space of homeomorphisms on a manifold
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by William E. Haver

Trans. Amer. Math. Soc. 195 (1974), 401-419

DOI: https://doi.org/10.1090/S0002-9947-1974-0362375-0

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Abstract:

The space, $\bar H(M)$, of all mappings of the compact manifold M onto itself which can be approximated arbitrarily closely by homeomorphisms is studied. It is shown that $\bar H(M)$ is homogeneous and weakly locally contractible. If M is a compact 2-manifold without boundary, then $\bar H(M)$ is shown to be locally contractible.

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