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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Homeomorphism groups of some direct limit spaces


Author: Margie Hale
Journal: Proc. Amer. Math. Soc. 85 (1982), 661-665
MSC: Primary 57S05; Secondary 54H15, 57N20, 58B05
DOI: https://doi.org/10.1090/S0002-9939-1982-0660625-4
MathSciNet review: 660625
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Abstract: Let $F$ be either of the spaces ${R^\infty } = {R^n}$ or ${Q^\infty } = {Q^n}$ where $R$ denotes the reals and $Q$ the Hilbert cube. Let $\mathcal {H}(M)$ be the homeomorphism group of a connected $F$-manifold $M$ with the compact-open topology. We prove that $\mathcal {H}(M)$ is separable, LindelΓΆf, paracompact, non-first-countable, and not a $k$-space.


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Keywords: Homeomorphism group, direct limit, compact-open topology, manifold
Article copyright: © Copyright 1982 American Mathematical Society