# Category:Separation Axioms

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This category contains results about the Tychonoff separation axioms.

Definitions specific to this category can be found in Definitions/Separation Axioms.

The **Tychonoff separation axioms** are a classification system for topological spaces.

They are not axiomatic as such, but they are conditions that may or may not apply to general or specific topological spaces.

## Subcategories

This category has the following 20 subcategories, out of 20 total.

### C

- Completely Normal Spaces (15 P)

### F

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

### H

### N

### P

### R

### S

- Semiregular Spaces (5 P)

### T

- T1/2 Spaces (2 P)
- T3 1/2 Spaces (12 P)
- Tychonoff Spaces (6 P)

### U

- Urysohn Functions (3 P)
- Urysohn Spaces (4 P)

## Pages in category "Separation Axioms"

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

### D

### E

- Equivalence of Definitions of Completely Hausdorff Space
- Equivalence of Definitions of Points Separated by Neighborhoods
- Equivalence of Definitions of Sets Separated by Neighborhoods
- Equivalence of Definitions of T2 Space
- Existence of Compact Hausdorff Space which is not T5
- Existence of Compact Space which Satisfies No Separation Axioms
- Existence of Completely Normal Space whose Product Space is Not Normal
- Existence of Hausdorff Space which is not Completely Hausdorff
- Existence of Hausdorff Space which is not T3, T4 or T5
- Existence of Normal Space which is not Completely Normal
- Existence of Regular Space which is not Tychonoff
- Existence of T4 Space which is not T3 1/2
- Existence of Topological Space which satisfies no Separation Axioms
- Existence of Topological Space which satisfies no Separation Axioms but T0
- Existence of Topological Space which satisfies no Separation Axioms but T0 and T1
- Existence of Topological Space which satisfies no Separation Axioms but T3
- Existence of Topological Space which satisfies no Separation Axioms but T4
- Existence of Tychonoff Space which is not Normal

### S

- Separation Axioms on Double Pointed Topology
- Separation Axioms Preserved under Homeomorphism
- Separation Properties in Open Extension of Particular Point Topology
- Separation Properties Not Preserved by Expansion
- Separation Properties of Alexandroff Extension of Rational Number Space
- Separation Properties Preserved by Expansion
- Separation Properties Preserved in Subspace
- Separation Properties Preserved in Subspace/Corollary
- Separation Properties Preserved under Topological Product
- Separation Properties Preserved under Topological Product/Corollary
- Sequence of Implications of Separation Axioms