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 25 subcategories, out of 25 total.
C
- Completely Normal Spaces (15 P)
F
- Fully Normal Spaces (4 P)
H
N
P
- Perfectly Normal Spaces (8 P)
R
S
- Semiregular Spaces (5 P)
- Separated by Closed Neighborhoods (empty)
- Separated by Function (empty)
- Separated by Neighborhoods (empty)
T
- T1/2 Spaces (2 P)
- T3 1/2 Spaces (12 P)
- Tychonoff Spaces (6 P)
U
- Urysohn Spaces (4 P)
Pages in category "Separation Axioms"
The following 35 pages are in this category, out of 35 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