Editing Separated sets (section)

==Relation to separation axioms and separated spaces==
{{main|separation axiom}}

The ''separation axioms'' are various conditions that are sometimes imposed upon topological spaces, many of which can be described in terms of the various types of separated sets. As an example we will define the T<sub>2</sub> axiom, which is the condition imposed on separated spaces. Specifically, a topological space is ''separated'' if, given any two [[distinct (mathematics)|distinct]] points ''x'' and ''y'', the singleton sets {''x''} and {''y''} are separated by neighbourhoods.

Separated spaces are usually called ''[[Hausdorff space]]s'' or ''T<sub>2</sub> spaces''.