Filter characterizations of 𝐶- and 𝐶*-embeddings

Green, John William

doi:10.1090/S0002-9939-1972-0303497-3

Filter characterizations of $C$- and $C^{\ast }$-embeddings
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Proc. Amer. Math. Soc. 35 (1972), 574-580 Request permission

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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