A characterization of real-compactness
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Abstract:
Let $\mathcal {Z}$ be a countably productive normal base in a Tychonoff space. We use proximity and construct a new Wallman-type realcompactification ${\eta ^\ast }(\mathcal {Z})$ which is always realcompact. A Tychonoff space is realcompact iff it has a countably productive normal base $\mathcal {Z}$ such that each $\mathcal {Z}$-ultrafilter with weakly countable intersection property is fixed.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 50 (1975), 412-418
- MSC: Primary 54D60; Secondary 54E05
- DOI: https://doi.org/10.1090/S0002-9939-1975-0391017-X
- MathSciNet review: 0391017