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 an Alexandrov space.

A T₁ space is locally finite if and only if it is discrete.

References

• Nakaoka, Fumie; Oda, Nobuyuki (2001), "Some applications of minimal open sets", International Journal of Mathematics and Mathematical Sciences, 29 (8): 471–476, doi:10.1155/S0161171201006482