uniform base

Let $X$ be a Hausdorff topological space. A basis for $X$ is said to be a uniform base if for all $x\in X$ and every neighborhood $U$ 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 $\frac{1}{n}$ form a uniform base of $X$.

Any uniform base of $X$ is a point countable base.

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