A family of subsets of a topological space such that every point has a neighborhood which intersects only a finite number of them.
Locally Finite Family
See also
Sigma-Locally Finite FamilyThis entry contributed by Margherita Barile
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Barile, Margherita. "Locally Finite Family." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/LocallyFiniteFamily.html