Physical Sciences and Mathematics Commons^™

Oif Spaces, Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, David Lutzer, Joe D. Mashburn

Mathematics Faculty Publications

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.