# Category:T3 Spaces

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This category contains results about **$T_3$ spaces** in the context of **Topology**.

$T = \struct {S, \tau}$ is a **$T_3$ space** if and only if:

- $\forall F \subseteq S: \relcomp S F \in \tau, y \in \relcomp S F: \exists U, V \in \tau: F \subseteq U, y \in V: U \cap V = \O$

That is, for any closed set $F \subseteq S$ and any point $y \in S$ such that $y \notin F$ there exist disjoint open sets $U, V \in \tau$ such that $F \subseteq U$, $y \in V$.

## Subcategories

This category has the following 5 subcategories, out of 5 total.

## Pages in category "T3 Spaces"

The following 36 pages are in this category, out of 36 total.

### C

### E

### L

### T

- T3 1/2 Space is T3 Space
- T3 Lindelöf Space is Fully T4 Space
- T3 Lindelöf Space is T4 Space
- T3 Property is Hereditary
- T3 Space is Fully T4 iff Paracompact
- T3 Space is Preserved under Homeomorphism
- T3 Space is Semiregular
- T3 Space with Sigma-Locally Finite Basis is Paracompact
- T3 Space with Sigma-Locally Finite Basis is Perfectly T4 Space
- T3 Space with Sigma-Locally Finite Basis is T4 Space
- T4 and T3 Space is T 3 1/2