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Proceedings of the American Mathematical Society

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

 

 

Localy compact full homeomorphism groups are zero-dimensional


Author: James Keesling
Journal: Proc. Amer. Math. Soc. 29 (1971), 390-396
MSC: Primary 54.80
MathSciNet review: 0275404
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Abstract: Let X be a metric space and let $ G(X)$ be the space of homeomorphisms of X with the compact open topology.

If $ G(X)$ is locally compact, then it is zero-dimensional.

Some examples are also given of metric spaces X for which $ G(X)$ is compact.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0275404-2
Keywords: Function space, compact open topology, space of homeomorphisms, flow, topological group, one parameter subgroup, locally compact topological group, zero-dimensional
Article copyright: © Copyright 1971 American Mathematical Society