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.

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
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.