Normal space
Type of topological space / From Wikipedia, the free encyclopedia
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For normal vector space, see normal (geometry).
In topology and related branches of mathematics, a normal space is a topological space X that satisfies Axiom T4: every two disjoint closed sets of X have disjoint open neighborhoods. A normal Hausdorff space is also called a T4 space. These conditions are examples of separation axioms and their further strengthenings define completely normal Hausdorff spaces, or T5 spaces, and perfectly normal Hausdorff spaces, or T6 spaces.
Quick Facts Separation axioms in topological spaces, Kolmogorov classification ...
Separation axioms in topological spaces | |
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Kolmogorov classification | |
T0 | (Kolmogorov) |
T1 | (Fréchet) |
T2 | (Hausdorff) |
T2½ | (Urysohn) |
completely T2 | (completely Hausdorff) |
T3 | (regular Hausdorff) |
T3½ | (Tychonoff) |
T4 | (normal Hausdorff) |
T5 | (completely normal Hausdorff) |
T6 | (perfectly normal Hausdorff) |
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