Back فضاء تيكونوف Arabic Пространство на Тихонов Bulgarian Vollständig regulärer Raum German Espacio de Tíjonov Spanish فضای تیخونوف Persian Espace complètement régulier French מרחב רגולרי לחלוטין HE Spazio di Tichonov Italian 티호노프 공간 Korean Tychonov-ruimte Dutch
| 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 branches of mathematics, Tychonoff spaces and completely regular spaces are kinds of topological spaces. These conditions are examples of separation axioms. A Tychonoff space is any completely regular space that is also a Hausdorff space; there exist completely regular spaces that are not Tychonoff (i.e. not Hausdorff).
Paul Urysohn had used the notion of completely regular space in a 1925 paper[1] without giving it a name. But it was Andrey Tychonoff who introduced the terminology completely regular in 1930.[2]
- ^ Urysohn, Paul (1925). "Über die Mächtigkeit der zusammenhängenden Mengen". Mathematische Annalen. 94 (1): 262–295. doi:10.1007/BF01208659. See pages 291 and 292.
- ^ Tychonoff, A. (1930). "Über die topologische Erweiterung von Räumen". Mathematische Annalen. 102 (1): 544–561. doi:10.1007/BF01782364.
© MMXXIII Rich X Search. We shall prevail. All rights reserved. Rich X Search