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Left Inverse


Given a map f:S->T between sets S and T, the map g:T->S is called a left inverse to f provided that g degreesf=id_S, that is, composing f with g from the left gives the identity on S. 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.


See also

Inverse, Right Inverse

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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Left Inverse

Cite this as:

Hedegaard, Rasmus. "Left Inverse." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/LeftInverse.html

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