Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Wallman-type compactifications and products


Author: Frank Kost
Journal: Proc. Amer. Math. Soc. 29 (1971), 607-612
MSC: Primary 54.53
MathSciNet review: 0281159
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Y is a Wallman-type compactification (O. Frink, Amer. J. Math. 86 (1964), 602-607) of X in case there is a normal base Z for the closed sets of X such that the ultrafilter space from Z, denoted $ \omega (Z)$, is topologically Y. It is not known if every compactification is Wallman-type. For $ {Z_\alpha }$ a normal base for the closed sets of $ {X_\alpha }$ for each a belonging to an index set $ \Delta $ it is shown that the Tychonoff product space $ {\prod _{\alpha \in \Delta }}\omega ({Z_\alpha })$ is a Wallman compactification of $ {\prod _{\alpha \in \Delta }}{X_\alpha }$. Also for $ X \subset T \subset \omega (Z)$ with Z a normal base for the closed sets of X, a proof that $ \omega (Z)$ is a Wallman-type compactification of T is indicated.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.53

Retrieve articles in all journals with MSC: 54.53


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0281159-8
PII: S 0002-9939(1971)0281159-8
Keywords: Wallman-type compactification, normal base, zero set, free ultrafilter
Article copyright: © Copyright 1971 American Mathematical Society