Category:Separation Axioms

H

• [+] Hausdorff Spaces‎ (2 C, 33 P)

N

• [+] Normal Spaces‎ (3 C, 9 P)

P

• [+] Perfectly T4 Spaces‎ (1 C, 4 P)

R

• [×] Regular Spaces‎ (10 P)

T

• [×] T0 Spaces‎ (17 P)
• [×] T1 Spaces‎ (29 P)
• [×] T3 1/2 Spaces‎ (8 P)
• [×] T3 Spaces‎ (24 P)

T cont.

• [+] T4 Spaces‎ (1 C, 24 P)
• [×] T5 Spaces‎ (21 P)
• [×] Tychonoff Spaces‎ (4 P)

U

• [×] Urysohn Spaces‎ (3 P)

C

• Cantor Space Satisfies All Separation Axioms

D

• Discrete Space Satisfies All Separation Properties
• Double Pointed Countable Complement Topology Fulfils no Separation Axioms
• Double Pointed Finite Complement Topology Fulfils no Separation Axioms

M

• Metric Space Fulfils All Separation Axioms

R

• Real Number Space Satisfies All Separation Axioms

S

• Separation Axioms on Double Pointed Topology
• Separation Axioms Preserved under Homeomorphism
• Separation Properties in Open Extension of Particular Point Topology
• Separation Properties Preserved by Expansion

S cont.

• Separation Properties Preserved in Subspace
• Separation Properties Preserved under Topological Product
• Sequence of Implications of Separation Axioms