uniform base

Let X be a Hausdorff topological space. A basis for X is said to be a uniform base if for all xX and every neighborhoodMathworldPlanetmathPlanetmath U of x, only a finite number of the basis sets containing x intersect the complement of U.

For example, in any metric space, the open balls of radius 1n form a uniform base of X.

Any uniform base of X is a point countable base.


  • 1 Steen, Lynn Arthur and Seebach, J. Arthur, Counterexamples in Topology, Dover Books, 1995.
Title uniform base
Canonical name UniformBase
Date of creation 2013-03-22 14:49:56
Last modified on 2013-03-22 14:49:56
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 4
Author mathcam (2727)
Entry type Definition
Classification msc 54E35