 If formula_158 is a metric map between metric spaces (that is, formula_159 for all "x", "y") satisfying "f"("x")="f"("y") whenever formula_160 then the induced function formula_161, given by formula_162, is a metric map formula_163

A topological space is sequential if and only if it is a quotient of a metric space.The ordered set formula_165 can be seen as a category by requesting exactly one morphism formula_166 if formula_167 and none otherwise.By using formula_168 as the tensor product and formula_24 as the identity, it becomes a monoidal category formula_170.