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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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

Author: John William Green
Journal: Proc. Amer. Math. Soc. 35 (1972), 574-580
MSC: Primary 54C45
MathSciNet review: 0303497
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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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Keywords: Stone-Čech compactification, z-filter, completely regular filter, $ {C^ \ast }$-embedding, C-embedding
Article copyright: © Copyright 1972 American Mathematical Society

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