uniform base
Let X be a Hausdorff topological space. A basis for X is said to be a uniform base if for all x∈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 1n 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 |