Assertion: global isometry | /r/Synonym | surjective isometries
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Source sentences:
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).