Assertion: isometry | /r/HasProperty | injection
Facets:
value: between metric spaces
type: LOCATION
value: necessarily
type: MANNER
Source sentences:
text: Since for any metric we have whenever , it follows that every isometry must be an injection.
text: Between metric spaces, isometries are necessarily injections and bijective isometries necessarily have isometries as inverses, so global isometries between metric spaces are also called surjective isometries; this does not work for Riemannian manifolds (where the inverse of an isometry need not be a morphism of manifolds), nor does it work for pseudometric spaces (where an isometry need not be injective).