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Locally finite space

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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.

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
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