Assertion: isomorphism | /r/HasProperty | map
Facets:
value: in mathematics
type: OTHER
value: to another object
type: TRANSITIVE-OBJECT
value: from one object
type: LOCATION
value: informally
type: MANNER
Source sentences:
text: Informally, an isomorphism is a map that preserves sets and relations among elements.
text: In mathematics, an isomorphism is a mapping between two structures of the same type that can be reversed by an inverse mapping.
text: "In mathematics, an isomorphism is a map from one object X to another object Y under which the structure on X corresponds exactly to the structure on Y. More precisely, ...
text: One thing about "relationship": it sounds as though what is being described is isomorphic structures (i.e. two structures for which there exists an isomorphism between them) rather than an isomorphism (a map between two structures).
text: An isomorphism is a map (which is bijective and has various nice properties but we'll leave those aside for a minute) which basically keeps everything the same.
text: Thus, the subject of the article is the presentation of a previously unknown method for determining the inverse for maps non-invertible in the usual sense, forming a composition commuting some isomorphism—a map invertible in the traditional sense.
text: First, the phrase "order isomorphism of po-groups" sounds redundant: in my experience, the usual thing in mathematical writing would be to write "isomorphism of po-groups," with the understanding that an "isomorphism of [things]" is a map that preserves the defining properties of the [things].