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Proceedings of the American Mathematical Society

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

 

 

Semiuniform spaces and topological homeomorphism groups


Author: R. V. Fuller
Journal: Proc. Amer. Math. Soc. 26 (1970), 365-368
MSC: Primary 54.30
DOI: https://doi.org/10.1090/S0002-9939-1970-0264595-4
MathSciNet review: 0264595
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Abstract: A well-known sufficient condition that a group of homeomorphisms, $ H$, from a topological space $ X$ onto itself be a topological group relative to the topology of pointwise convergence is that $ X$ be uniformizable and $ H$ be equicontinuous.

In this paper we prove an analogous condition in which the space $ X$ is assumed to be only regular instead of completely regular (uniformizable). This is accomplished by means of the concepts of semiuniformity and semiequicontinuity introduced here.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0264595-4
Keywords: Semiuniformity, semiequicontinuity, uniform semiuniformity, semitopological group
Article copyright: © Copyright 1970 American Mathematical Society