Editing T1 space (section)

==Generalisations to other kinds of spaces==
The terms "T<sub>1</sub>", "R<sub>0</sub>", and their synonyms can also be applied to such variations of topological spaces as [[uniform space]]s, [[Cauchy space]]s, and [[convergence space]]s.
The characteristic that unites the concept in all of these examples is that limits of fixed ultrafilters (or constant [[net (topology)|net]]s) are unique (for T<sub>1</sub> spaces) or unique up to topological indistinguishability (for R<sub>0</sub> spaces).

As it turns out, uniform spaces, and more generally Cauchy spaces, are always R<sub>0</sub>, so the T<sub>1</sub> condition in these cases reduces to the T<sub>0</sub> condition.
But R<sub>0</sub> alone can be an interesting condition on other sorts of convergence spaces, such as [[pretopological space]]s.