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
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