T1 space
Topological space in which all singleton sets are closed / From Wikipedia, the free encyclopedia
In topology and related branches of mathematics, a T1 space is a topological space in which, for every pair of distinct points, each has a neighborhood not containing the other point.[1] An R0 space is one in which this holds for every pair of topologically distinguishable points. The properties T1 and R0 are examples of separation axioms.
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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