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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Uniqueness results for homeomorphism groups


Author: Robert R. Kallman
Journal: Trans. Amer. Math. Soc. 295 (1986), 389-396
MSC: Primary 57S05; Secondary 22A05, 54H05, 54H15, 58D05
MathSciNet review: 831205
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0831205-0
PII: S 0002-9947(1986)0831205-0
Keywords: Complete separable metric group, homeomorphism group, diffeomorphism group, manifold, Cantor set, Hilbert cube
Article copyright: © Copyright 1986 American Mathematical Society