Title

OIF Spaces

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

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.

Publisher

Symposium of General Topology

Volume

18

Issue

2

Volume

18

Issue

2

Peer Reviewed

yes

Keywords

Open-in-Finite (OIF) base, strong OIF base, hereditary OIF space, uniform base, metrizable

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