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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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, $ \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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Additional Information

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