Definition:Kolmogorov Space
(Redirected from Definition:T0 Space)
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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.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): T-axioms or Tychonoff conditions: 0. ($T_0$-space or Kolmogorov Space)
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Kolmogorov space