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Proceedings of the American Mathematical Society

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Local connectedness and pseudocompactness in completely regular spaces

Author: Donald G. Hartig
Journal: Proc. Amer. Math. Soc. 68 (1978), 117-120
MSC: Primary 54D05
MathSciNet review: 0461425
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Abstract: The properties of local connectedness and pseudocompactness of a completely regular space X are characterized via algebraic properties of the space $ C(X)$. These characterizations are then used to prove the (well-known) theorem that $ \beta X$ is locally connected if and only if X is locally connected and pseudocompact.

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Keywords: Completely regular, locally connected, pseudocompact, $ C(X)$, pointwise convergent, uniform convergent, Stone-Čech compactification
Article copyright: © Copyright 1978 American Mathematical Society

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