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)

 

Topological spaces with a $ \sigma $-point finite base


Author: C. E. Aull
Journal: Proc. Amer. Math. Soc. 29 (1971), 411-416
MSC: Primary 54.50
MathSciNet review: 0281154
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The principal results of the paper are as follows. A topological space with a $ \sigma $-point finite base has a $ \sigma $-disjoint base if it is either hereditarily collectionwise normal or hereditarily screenable. From a metrization theorem of Arhangel'skiĭ, it follows that a $ {T_1}$-space with a $ \sigma $-point finite base is metrizable iff it is perfectly normal and collectionwise normal. A topological space with a $ \sigma $-point base is quasi-developable in the sense of Bennett. Consequently a theorem of Čoban follows that for a topological space $ (X,\Im )$ the following are equivalent: (a) $ (X,\Im )$ is a metacompact normal Moore space, (b) $ (X,\Im )$ is a perfectly normal $ {T_1}$-space with a $ \sigma $-point finite base.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.50

Retrieve articles in all journals with MSC: 54.50


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0281154-9
PII: S 0002-9939(1971)0281154-9
Keywords: $ \sigma $-point finite base, $ \sigma $-disjoint base, quasi-development, Moore space, hereditarily collectionwise normal, hereditarily screenable, metacompact or pointwise paracompact, subparacompact or $ {F_\sigma }$-screenable
Article copyright: © Copyright 1971 American Mathematical Society