Editing T1 space (section)

==Definitions==
Let ''X'' be a [[topological space]] and let ''x'' and ''y'' be points in ''X''. We say that ''x'' and ''y'' are {{em|[[Separated sets|separated]]}} if each lies in a [[neighbourhood (mathematics)|neighbourhood]] that does not contain the other point.
* ''X'' is called a '''T<sub>1</sub> space''' if any two distinct points in ''X'' are separated.
* ''X'' is called an '''R<sub>0</sub> space''' if any two [[topologically distinguishable]] points in ''X'' are separated.

A T<sub>1</sub> space is also called an '''accessible space''' or a space with '''Fréchet topology''' and an R<sub>0</sub> space is also called a '''symmetric space'''. (The term {{em|Fréchet space}} also has an [[Fréchet space|entirely different meaning]] in [[functional analysis]]. For this reason, the term ''T<sub>1</sub> space'' is preferred. There is also a notion of a [[Fréchet–Urysohn space]] as a type of [[sequential space]]. The term {{em|symmetric space}} also has [[Symmetric space|another meaning]].)

A topological space is a T<sub>1</sub> space if and only if it is both an R<sub>0</sub> space and a [[Kolmogorov space|Kolmogorov (or T<sub>0</sub>) space]] (i.e., a space in which distinct points are topologically distinguishable). A topological space is an R<sub>0</sub> space if and only if its [[Kolmogorov quotient]] is a T<sub>1</sub> space.