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
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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