point countable base

Let X be a topological spaceMathworldPlanetmath. A basis of X is a point countable base if every point of X is contained in at most countably many sets of .

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.


  • 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