Abstract:A subset $S$ of a topological space is said to be conditionally compact if every infinite subset of $S$ has a limit point in the space. If a space has a dense conditionally compact subset, it follows that it is pseudocompact, but the converse is not true. Examples are given of spaces that are pseudocompact, do not have dense conditionally compact subsets, but do have compactifications that are products of first countable spaces. For locally compact spaces, though, with such compactifications, the continuum hypothesis implies that pseudocompactness is equivalent to having a dense conditionally compact subset. A locally compact pseudocompact space without a dense conditionally compact subset is described.
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- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 137-142
- MSC: Primary 54D30; Secondary 54D35, 54D45
- DOI: https://doi.org/10.1090/S0002-9939-1981-0589156-6
- MathSciNet review: 589156