Editing Approach space (section)

==Categorical properties==

The main interest in approach spaces and their contractions is that they form a [[category (mathematics)|category]] with good properties, while still being quantitative like metric spaces. One can take arbitrary [[Product (category theory)|products]], [[Coproduct|coproducts]], and quotients, and the results appropriately generalize the corresponding results for topologies. One can even "distancize" such badly non-metrizable spaces like β'''N''', the [[Stone–Čech compactification]] of the integers.

Certain hyperspaces, [[measure space|measure spaces]], and [[Probabilistic metric space|probabilistic metric spaces]] turn out to be naturally endowed with a distance. Applications have also been made to [[approximation theory]].