# Completely Regular Space

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A topological space $X$ is said to be completely regular if one-point sets are closed in $X$ and if for each point $x_0$ and each closed set $A$ not containing $x_0$, there is a continuous function $f : X \to [0,1]$ such that $f(x_0) = 1$ and $f(A) = {0}$.[1]