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 PointCountableBase 2013-03-22 14:49:59 2013-03-22 14:49:59 mathcam (2727) mathcam (2727) 4 mathcam (2727) Definition msc 54E35