Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1972-0303497-3
MathSciNet review: 0303497
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54C45

Retrieve articles in all journals with MSC: 54C45


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0303497-3
Keywords: Stone-Čech compactification, z-filter, completely regular filter, $ {C^ \ast }$-embedding, C-embedding
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society