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Right Inverse


Given a map f:S->T between sets S and T, the map g:T->S is called a right inverse to f provided that f degreesg=id_T, that is, composing f with g from the right gives the identity on T. Often f is a map of a specific type, such as a linear map between vector spaces, or a continuous map between topological spaces, and in each such case, one often requires a right inverse to be of the same type as that of f.

If f has a right inverse, then f is surjective. Conversely, if f is surjective and the axiom of choice is assumed, then f has a right inverse, at least as a set mapping.


See also

Inverse, Left Inverse, Surjection

Portions of this entry contributed by John Derwent

Portions of this entry contributed by Rasmus Hedegaard

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References

Lee, J. M. Introduction to Topological Manifolds. New York: Springer, 2000.Mac Lane, S. and Birkhoff, G. §1.2 in Algebra, 3rd ed. Providence, RI: Amer. Math. Soc., 1999.

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Right Inverse

Cite this as:

Derwent, John; Hedegaard, Rasmus; and Weisstein, Eric W. "Right Inverse." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RightInverse.html

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