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Local Connectedness of the stone-Čech Compactification

Published online by Cambridge University Press:  20 November 2018

D. Baboolal
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 V ⊂ U such that V[x] is connected for each x ∈ X. 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.

Keywords

Uniform local connectednessproperty S54D0554D3554E15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 2 , 01 June 1988 , pp. 236 - 240
Copyright
Copyright © Canadian Mathematical Society 1988

References

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