Title
Document Type
Article
Publication Date
2000
Publication Source
Questions and Answers in General Topology
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
Volume
18
Issue
2
Peer Reviewed
yes
Keywords
Open-in-Finite (OIF) base, strong OIF base, hereditary OIF space, uniform base, metrizable
eCommons Citation
Balogh, Zoltan; Bennett, Harold; Burke, Dennis; Gruenhage, Gary; Lutzer, David; and Mashburn, Joe D., "OIF Spaces" (2000). Mathematics Faculty Publications. 19.
https://ecommons.udayton.edu/mth_fac_pub/19
Comments
Document is made available for download with the permission of the publisher. It is the accepted manuscript version. Some differences may exist between this version and the published version; as such, researchers wishing to quote directly from this source are advised to consult the the version of record.
Permission documentation is on file.