- Separation axiom - Wikipedia
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 axioms only in the sense that, when defining the notion of topological space, you could add these conditions as extra axioms to get a more restricted notion of what a topological space is. The modern approach is to fix once and for all the axiomatization of topological space and then speak of kinds of topological spaces.
in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups with axiom axioms concept fundamental math mathematical mathematics separation topology wiki wikipedia
Note: See also: The precise meanings of the terms associated with the separation axioms has varied over time, as explained in History of the separation axioms... http://en.wikipedia.org/wiki/History_of_the_separation_axioms
separation from all users