Geodesic
Local Connectedness of the stone-Čech Compactification
Canadian mathematical bulletin, Tome 31 (1988) no. 2, pp. 236-240

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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.
DOI : 10.4153/CMB-1988-036-2
Mots-clés : Uniform local connectedness, property S, 54D05, 54D35, 54E15 
Baboolal, D. Local Connectedness of the stone-Čech Compactification. Canadian mathematical bulletin, Tome 31 (1988) no. 2, pp. 236-240. doi: 10.4153/CMB-1988-036-2
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     title = {Local {Connectedness} of the {stone-\v{C}ech} {Compactification}},
     journal = {Canadian mathematical bulletin},
     pages = {236--240},
     year = {1988},
     volume = {31},
     number = {2},
     doi = {10.4153/CMB-1988-036-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-036-2/}
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