# Definition:Kolmogorov Space

## Definition

Let $T = \left({S, \tau}\right)$ be a topological space.

### Definition 1

$\left({S, \tau}\right)$ is a Kolmogorov space or $T_0$ space if and only if:

$\forall x, y \in S$ such that $x \ne y$, either:
$\exists U \in \tau: x \in U, y \notin U$
or:
$\exists U \in \tau: y \in U, x \notin U$

### Definition 2

$\left({S, \tau}\right)$ is a Kolmogorov space or $T_0$ space if and only if no two points can be limit points of each other.

## Also see

• Results about $T_0$ spaces can be found here.

## Source of Name

This entry was named for Andrey Nikolaevich Kolmogorov.