A collectionMathworldPlanetmath 𝒰 of subsets of a topological spaceMathworldPlanetmath X is said to be point-finite if every point of X lies in only finitely many members of 𝒰.

Compare this to the stronger property of being locally finitePlanetmathPlanetmathPlanetmath.

Point-finiteness is used in the definition of metacompactness.

Title point-finite
Canonical name Pointfinite
Date of creation 2013-03-22 16:17:02
Last modified on 2013-03-22 16:17:02
Owner yark (2760)
Last modified by yark (2760)
Numerical id 5
Author yark (2760)
Entry type Definition
Classification msc 54A99
Synonym point finite
Related topic LocallyFinite
Related topic Metacompact
Defines point finite collection
Defines point-finite collection
Defines point finiteness
Defines point-finiteness