Separation axioms | Topology

Separation axiom

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 has varied over time. Especially in older literature, different authors might have different definitions of each condition. (Wikipedia).

Separation axiom
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Urysohn's lemma | Topological space | Star refinement | Equality (mathematics) | Functional analysis | Closure (topology) | Weak Hausdorff space | Topology | Continuous function | T1 space | Sober space | Base (topology) | Hausdorff space | Zermelo–Fraenkel set theory | Neighbourhood (mathematics) | Semiregular space | Urysohn and completely Hausdorff spaces | General topology | Fréchet space | Mathematics | Tychonoff space | Cocountable topology | Subset | Axiom | Regular space | History of the separation axioms | Regular open set | Normal space | Open set