Urysohn space

Definition
A topological space $$X$$ is termed a Urysohn space if given any two distinct points $$x,y \in X$$, there exists a continuous function $$f:X \to [0,1]$$ such that $$f(x) = 0$$, <math<f(y) = 1.

Facts

 * Natural map from topological space to max-spectrum of ring of continuous real-valued functions is an injection iff the space is Urysohn

Primary subject wiki link

 * Topospaces:Urysohn space