Editing Category of metric spaces (section)

==Arrows==
The [[monomorphism]]s in '''Met''' are the [[injective]] metric maps. The [[epimorphism]]s are the metric maps for which the [[Domain of a function|domain]] of the map has a [[Dense set|dense]] [[Image (mathematics)|image]] in the [[Range of a function|range]]. The [[isomorphism]]s are the [[Isometry|isometries]], i.e. metric maps which are injective, [[surjective]], and distance-preserving.

As an example, the inclusion of the [[rational number]]s into the [[real number]]s is a monomorphism and an epimorphism, but it is clearly not an isomorphism; this example shows that '''Met''' is not a [[balanced category]].