Local connectedness and pseudocompactness in completely regular spaces

Hartig, Donald G.

doi:10.1090/S0002-9939-1978-0461425-X

Local connectedness and pseudocompactness in completely regular spaces
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by Donald G. Hartig PDF

Proc. Amer. Math. Soc. 68 (1978), 117-120 Request permission

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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