Questions and Answers in General Topology
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.
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Symposium of General Topology
Open-in-Finite (OIF) base, strong OIF base, hereditary OIF space, uniform base, metrizable
Balogh, Zoltan; Bennett, Harold; Burke, Dennis; Gruenhage, Gary; Lutzer, David; and Mashburn, Joe D., "OIF Spaces" (2000). Mathematics Faculty Publications. 19.