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Local Connectedness of the stone-Čech Compactification

Published online by Cambridge University Press:  20 November 2018

D. Baboolal*
Affiliation:
Department of Mathematics, University of Durban-WestvillePrivate Bag X54001, Durban4000
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Abstract

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A uniform space X is said to be uniformly locally connected if given any entourage U there exists an entourage VU such that V[x] is connected for each xX. It is said to have property S if given any entourage U, X can be written as a finite union of connected sets each of which is U-small.

Based on these two uniform connection properties, another proof is given of the following well known result in the theory of locally connected spaces: The Stone-Čech compactification βX is locally connected if and only if X is locally connected and pseudocompact.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Baboolal, D. and Ori, R. G., On uniform connection properties, Comment. Math. Univ. Carolinae. 24, 4 (1983), pp. 747754.Google Scholar
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10. Whyburn, G. T., Analytic topology, Amer. Math. Soc. Colloq. Publ. Vol. 28 (1942).Google Scholar
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