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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- Taqdir Husain, Introduction to topological groups, W. B. Saunders Co., Philadelphia, Pa.-London, 1966. MR 0200383
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Keywords:
Semiuniformity,
semiequicontinuity,
uniform semiuniformity,
semitopological group
Article copyright:
© Copyright 1970
American Mathematical Society