Article
OIF Spaces
Questions and Answers in General Topology
Document Type
Article
Publication Date
1-1-2000
Abstract
A base β of a space X is called an OIF base when every element of B is a subset of only a finite number of other elements of β. We will explore the fundamental properties of spaces having such bases. In particular, we will show that in T2 spaces, strong OIF bases are the same as uniform bases, and that in T3 spaces where all subspaces have OIF bases, compactness, countable compactness, or local compactness will give metrizability.
Inclusive pages
129-141
ISBN/ISSN
0918-4732
Document Version
Postprint
Copyright
Copyright © 2008-2015, Symposium of General Topology.
Publisher
Symposium of General Topology
Peer Reviewed
Yes
Keywords
- Open-in-Finite (OIF) base,
- strong OIF base,
- hereditary OIF space,
- uniform base,
- metrizable
Disciplines
Citation Information
Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, et al.. "OIF Spaces" Questions and Answers in General Topology Vol. 18 Iss. 2 (2000) Available at: http://works.bepress.com/joe_mashburn/8/
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Permission documentation is on file.