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 |
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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 |