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Separation Axiom

Separation Axiom

Dec 05, 20251 min read

  • math/topology

Definition

The separation axioms are properties of topological spaces that characterize how distinct points and closed sets can be separated by open sets. These axioms form a hierarchy of increasingly stronger conditions:

T0 Space (Kolmogorov Space)

T1 Space

T2 Space (Hausdorff Space)

T3 Space (Regular Space)

T3.5 Space (Completely Regular Space)

T4 Space (Normal Space)

T5 Space (Completely Normal Space)

T6 Space (Perfectly Normal Space)


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