## Filter characterizations of $C$- and $C^{\ast }$-embeddings

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- by John William Green
- Proc. Amer. Math. Soc.
**35**(1972), 574-580 - DOI: https://doi.org/10.1090/S0002-9939-1972-0303497-3
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## Abstract:

A filter*F*on a space

*S*is completely regular if the complement of each set in

*F*is completely separated from some set in

*F*. A characterization of the Stone-Čech compactification due to Alexandroff is used to establish the following theorem. Suppose

*K*is a subspace of a Tychonoff space

*S*.

*K*is ${C^ \ast }$-embedded in

*S*if and only if the trace on

*K*of every maximal completely regular filter on

*S*intersecting

*K*is maximal completely regular on

*K*. A similar characterization of the

*C*-embedded subsets of a Tychonoff space is obtained as are several related results.

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## Bibliographic Information

- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**35**(1972), 574-580 - MSC: Primary 54C45
- DOI: https://doi.org/10.1090/S0002-9939-1972-0303497-3
- MathSciNet review: 0303497