General topology | Properties of topological spaces

Locally finite space

In the mathematical field of topology, a locally finite space is a topological space in which every point has a finite neighborhood, that is, an open neighborhood consisting of finitely many elements. A locally finite space is Alexandrov. A T1 space is locally finite if and only if it is discrete. (Wikipedia).

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Related pages

Neighbourhood (mathematics) | Topological space | Mathematics | Finite set | Topology | Alexandrov topology | Discrete space | T1 space