Separation axioms | Topological spaces | Topology

Tychonoff space

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 refers to any completely regular space that is also a Hausdorff space; there exist completely regular spaces that are not Tychonoff (i.e. not Hausdorff). Tychonoff spaces are named after Andrey Nikolayevich Tychonoff, whose Russian name (Тихонов) is variously rendered as "Tychonov", "Tikhonov", "Tihonov", "Tichonov", etc. who introduced them in 1930 in order to avoid the pathological situation of Hausdorff spaces whose only continuous real-valued functions are constant maps. (Wikipedia).

Tychonoff space
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Related pages

Topological manifold | Tychonoff cube | Topological space | Metric space | Separated sets | Closure (topology) | Stone–Čech compactification | Topology | Order topology | Mathematical analysis | Reflective subcategory | Topological group | Initial topology | CW complex | Pseudometric space | Quotient space (topology) | Category of topological spaces | Unit interval | Real closed ring | Moore plane | Hausdorff space | Uniform space | Bounded function | Final topology | Point (geometry) | Mathematics | Euclidean space | Category theory | Existential quantification | Functor | Tychonoff's theorem | Compactification (mathematics) | Regular space | Kolmogorov space | History of the separation axioms | Real algebraic geometry | Normal space | Separation axiom | Universal property | Realcompact space | Closed set