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