Meaning of completely regular space

complete'ly reg'ular space'

Pronunciation: [key]
— Math. Math.
  1. a topological space in which, for every point and a closed set not containing the point, there is a continuous function that has value 0 at the given point and value 1 at each point in the closed set.
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.