Definition:Kolmogorov Space

Definition
A topological space $\left({X, \vartheta}\right)$ is $T_0$ when for any two points $x, y \in X$ there exists an open set $U \in \vartheta$ which contains one of the points, but not the other.

That is, $\left({X, \vartheta}\right)$ is $T_0$ when for any two points $x, y \in X$ at least one of the following options happens:
 * $\exists U \in \vartheta: x \in U, y \notin U$
 * $\exists V \in \vartheta: y \in V, x \notin V$

That is:
 * $\left({X, \vartheta}\right)$ is $T_0$ if every two points in $X$ are topologically distinguishable.

Such a space is called a Kolmogorov space.