Definition:Kolmogorov Space

Definition

Let $T = \struct {S, \tau}$ be a topological space.

Definition 1

$\struct {S, \tau}$ 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

$\struct {S, \tau}$ 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.