Pseudocompactness and closed subsets of products

Author:
James E. Joseph

Journal:
Proc. Amer. Math. Soc. **74** (1979), 338-342

MSC:
Primary 54D30; Secondary 54C30, 54C99

MathSciNet review:
524313

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Abstract: This paper contains several new characterizations of arbitrary pseudocompact spaces, i.e. spaces characterized by the property that all continuous real-valued functions on the space are bounded. These characterizations parallel known characterizations of Hausdorff spaces including the useful and well-known result that a space *Y* is Hausdorff if and only if whenever and are continuous functions on a common domain into *Y* which agree on a dense subset of the domain.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1979-0524313-7

Keywords:
Pseudocompactness,
filterbases,
graphs

Article copyright:
© Copyright 1979
American Mathematical Society