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

MathSciNet review:
660625

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Abstract: Let be either of the spaces or where denotes the reals and the Hilbert cube. Let be the homeomorphism group of a connected -manifold with the compact-open topology. We prove that is separable, Lindelöf, paracompact, non-first-countable, and not a -space.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1982-0660625-4

Keywords:
Homeomorphism group,
direct limit,
compact-open topology,
manifold

Article copyright:
© Copyright 1982
American Mathematical Society