# 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 conditions that may or may not apply to general or specific topological spaces.

## Subcategories

This category has the following 19 subcategories, out of 19 total.

### C

### F

### H

### N

### P

### R

### S

### T

### U

## Pages in category "Separation Axioms"

The following 32 pages are in this category, out of 32 total.

### D

### E

- Equivalence of Definitions of T2 Space
- Existence of Compact Hausdorff Space which is not T5
- 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