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Proceedings of the American Mathematical Society

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

 
 

 

$R_{3}$-quasi-uniform spaces and topological homeomorphism groups


Author: Massood Seyedin
Journal: Proc. Amer. Math. Soc. 52 (1975), 465-468
MSC: Primary 54E15
DOI: https://doi.org/10.1090/S0002-9939-1975-0375245-5
MathSciNet review: 0375245
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Abstract: It is well known that if $X$ is a completely regular space and $G$ is a homeomorphism group of $X$ onto itself such that $G$ is equicontinuous with respect to a compatible uniformity of $X$, then $G$ is a topological group under the topology of pointwise convergence. In this paper, we obtain a generalization of the above result by means of ${R_3}$-quasi-uniformities.


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Keywords: <IMG WIDTH="30" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${R_3}$">-quasi-uniform space, quasi-equicontinuous, quasi-uniform cover, joint continuity
Article copyright: © Copyright 1975 American Mathematical Society