# 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.

## References

• 1 Steen, Lynn Arthur and Seebach, J. Arthur, Counterexamples in Topology, Dover Books, 1995.
Title uniform base UniformBase 2013-03-22 14:49:56 2013-03-22 14:49:56 mathcam (2727) mathcam (2727) 4 mathcam (2727) Definition msc 54E35