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In topology, a branch of mathematics, a retraction is a continuous mapping from a topological space into a subspace that preserves the position of all points in that subspace. [1] The subspace is then called a retract of the original space. A deformation retraction is a mapping that captures the idea of continuously shrinking a space into a ...
In mathematics, in the field of ... The normal complement, specifically, is the kernel of the retraction. ... additional terms may apply.
In fact, their earlier publications, up to, e.g., Mac Lane (1963)'s Homology, used the term right inverse. It was not until 1965 when Eilenberg and John Coleman Moore coined the dual term 'coretraction' that Borsuk's term was lifted to category theory in general. [3] The term coretraction gave way to the term section by the end of the 1960s.
The image of a retraction is called a retract of the original space. A retraction which is homotopic to the identity is known as a deformation retraction. This term is also used in category theory to refer to any split epimorphism. [citation needed] The scalar projection (or resolute) of one vector onto another.
2 Mathematics. 3 Human physiology. 4 Linguistics. 5 See also. Toggle the table of contents. Retraction. 2 languages. ... Retraction (kinesiology), an anatomical term ...
In mathematics, Sharafutdinov's retraction is a construction that gives a retraction of an open non-negatively curved Riemannian manifold onto its soul. It was first used by Sharafutdinov to show that any two souls of a complete Riemannian manifold with non-negative sectional curvature are isometric . [ 1 ]
A left inverse in mathematics may refer to: ... Retraction (category theory), ... additional terms may apply.
Depending on authors, the term "maps" or the term "functions" may be reserved for specific kinds of functions or morphisms (e.g., function as an analytic term and map as a general term). mathematics See mathematics. multivalued A "multivalued function” from a set A to a set B is a function from A to the subsets of B.