local base

Let x be a point in a topological spaceMathworldPlanetmath X. A local base around x, is a family of neighborhoodsMathworldPlanetmathPlanetmath 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