Back بديهية الفصل Arabic Axioma de separació Catalan Oddělovací axiom Czech Уйрăласлăх аксиомисем CV Trennungsaxiom German Apartiga aksiomo Esperanto Axiomas de separación Spanish Eralduvusaksioomid Estonian اصل جداسازی Persian Separaatio (matematiikka) Finnish
| Separation axioms in topological spaces | |
|---|---|
| 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) |
In topology and related fields of mathematics, there are several restrictions that one often makes on the kinds of topological spaces that one wishes to consider. Some of these restrictions are given by the separation axioms. These are sometimes called Tychonoff separation axioms, after Andrey Tychonoff.
The separation axioms are not fundamental axioms like those of set theory, but rather defining properties which may be specified to distinguish certain types of topological spaces. The separation axioms are denoted with the letter "T" after the German Trennungsaxiom ("separation axiom"), and increasing numerical subscripts denote stronger and stronger properties.
The precise definitions of the separation axioms have varied over time. Especially in older literature, different authors might have different definitions of each condition.
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