Category:T4 Spaces

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This category contains results about $T_4$ spaces in the context of Topology.

$T = \struct {S, \tau}$ is a $T_4$ space if and only if:

$\forall A, B \in \map \complement \tau, A \cap B = \O: \exists U, V \in \tau: A \subseteq U, B \subseteq V, U \cap V = \O$

That is, for any two disjoint closed sets $A, B \subseteq S$ there exist disjoint open sets $U, V \in \tau$ containing $A$ and $B$ respectively.

Subcategories

This category has the following 8 subcategories, out of 8 total.

E

Excluded Point Topology is T4‎ (4 P)

F

Fully Normal Spaces‎ (4 P)
Fully T4 Spaces‎ (6 P)

M

Metric Space is T4‎ (3 P)

N

Normal Spaces‎ (3 C, 18 P)

P

Perfectly T4 Spaces‎ (2 C, 5 P)

T

T3 Lindelöf Space is T4 Space‎ (3 P)
T3 Space with Sigma-Locally Finite Basis is T4 Space‎ (5 P)

Pages in category "T4 Spaces"

The following 34 pages are in this category, out of 34 total.

A

Alexandroff Extension which is T2 Space is also T4 Space

C

E

F

I

Indiscrete Space is T4

M

O

P

S

T

U

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Separation Axioms