point countable base
Let $X$ be a topological space^{}. A basis $\mathcal{B}$ of $X$ is a point countable base if every point of $X$ is contained in at most countably many sets of $\mathcal{B}$.
Any uniform base is a point countable base, and a theorem of R. W. Heath states that every semimetric space with a point countable base is developable.
References
- 1 Steen, Lynn Arthur and Seebach, J. Arthur, Counterexamples in Topology, Dover Books, 1995.
Title | point countable base |
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Canonical name | PointCountableBase |
Date of creation | 2013-03-22 14:49:59 |
Last modified on | 2013-03-22 14:49:59 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 4 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 54E35 |