Filter characterizations of 𝐶- and 𝐶*-embeddings-Reference-Cited by-同舟云学术

Filter characterizations of 𝐶- and 𝐶*-embeddings

Published:1972 Issue:2 Volume:35 Page:574-580
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Green John William

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 ∗ {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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1972-035-02/S0002-9939-1972-0303497-3/S0002-9939-1972-0303497-3.pdf

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