On the topological completion
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- by Howard Curzer and Anthony W. Hager PDF
- Proc. Amer. Math. Soc. 56 (1976), 365-370 Request permission
Abstract:
Let $X$ be a Tychonoff space. As is well known, the points of the Stone-Čech compactification $\beta X$ “are” the zero-set ultrafilters of $X$, and the points of the Hewitt real-compactification $\upsilon X$ are the zero-set ultrafilters which are closed under countable intersection. It is shown here that a zero-set ultrafilter is a point of the Dieudonné topological completion $\delta X$ iff the family of complementary cozero sets is $\sigma$-discretely, or locally finitely, additive. From this follows a characterization of those dense embeddings $X \subset Y$ such that each continuous metric space-valued function on $X$ extends over $Y$, and a somewhat novel proof of the Katětov-Shirota Theorem.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 56 (1976), 365-370
- MSC: Primary 54D60
- DOI: https://doi.org/10.1090/S0002-9939-1976-0415573-9
- MathSciNet review: 0415573