The closure of the space of homeomorphisms on a manifold

Author:
William E. Haver

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

MSC:
Primary 57E05; Secondary 57A20

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

MathSciNet review:
0362375

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

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

Keywords:
Spaces of homeomorphisms,
cellular mappings,
closure of the space of homeomorphisms,
compact manifolds,
infinite dimensional manifolds,
homogeneous spaces

Article copyright:
© Copyright 1974
American Mathematical Society