# local base

Let $x$ be a point in a topological space $X$. A local base around $x$, is a family of neighborhoods such that every neighborhood of $x$ contains a member of the family. A local base is also known as a neighborhood base.

 Title local base Canonical name LocalBase Date of creation 2013-03-22 12:22:16 Last modified on 2013-03-22 12:22:16 Owner yark (2760) Last modified by yark (2760) Numerical id 9 Author yark (2760) Entry type Definition Classification msc 54-00 Synonym base of a neighborhood system Synonym neighborhood base Synonym base of a neighbourhood system Synonym neighbourhood base Related topic FirstAxiomOfCountability Related topic Neighborhood Related topic NeighborhoodSystem