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 $f(x)=0$, $f(y)=1$.

Facts

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

External links

Primary subject wiki link

• Topospaces:Urysohn space