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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
DOI: https://doi.org/10.1090/S0002-9939-1979-0524313-7
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 $ \phi = \alpha $ whenever $ \phi $ and $ \alpha $ 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: https://doi.org/10.1090/S0002-9939-1979-0524313-7
Keywords: Pseudocompactness, filterbases, graphs
Article copyright: © Copyright 1979 American Mathematical Society

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