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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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