Separation axiom
![An illustration of some of the separation axioms. A blue region indicates an open set, a red rectangle a closed set, and a black dot a point.](/Images/godic/202502/10/Separation_axioms_illustrated4442.png")
![](/Images/godic/202502/10/Separation_axioms4442.png")
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.