Assertion: isometry | /r/HasProperty | injective
Facets:
value: automatically
type: MANNER
value: always
type: TEMPORAL
value: earlier in the article
type: TEMPORAL
Source sentences:
text: An isometry is automatically injective; otherwise two distinct points, a and b, could be mapped to the same point, thereby contradicting the coincidence axiom of the metric
text: Okay, but the fact remains that earlier in the article, "isometry" is said to be automatically injective.
text: Isometries are injective
text: To prove that an isometry is injective is easy:
text: An isometry is automatically injective and continuous.
text: All isometries are injective.
text: All isometries are injective.
text: Although every isometry must be injective, however, it is not necessarily a bijection, and so might not have an inverse.
text: Isometries are always injective; the image of a compact or complete set under an isometry is compact or complete, respectively.