# Category:T0 Spaces

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This category contains results about T0 Spaces in the context of Topology.

$\left({S, \tau}\right)$ 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:
- $\exists U \in \tau: y \in U, x \notin U$

## Subcategories

This category has the following 4 subcategories, out of 4 total.

### D

### E

### P

### R

## Pages in category "T0 Spaces"

The following 31 pages are in this category, out of 31 total.

### C

### E

- Either-Or Topology is T0
- Equivalence of Definitions of T0 Space
- Excluded Point Space is T0
- Excluded Set Topology is not T0
- Existence of Hausdorff Space which is not T3, T4 or T5
- Existence of Topological Space which satisfies no Separation Axioms but T0
- Existence of Topological Space which satisfies no Separation Axioms but T0 and T1