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Retract


A subspace A of X is called a retract of X if there is a continuous map f:X->X (called a retraction) such that for all x in X and all a in A,

1. f(x) in A, and

2. f(a)=a.

Equivalently, a subspace A of X is called a retract of X if there is a continuous map f:X->A (called a retraction) such that for all a in A,

 f(a)=a.

See also

Absolute Retract, Deformation Retract, Retraction, Strong Deformation Retract

Portions of this entry contributed by Jonathan Sondow (author's link)

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Cite this as:

Sondow, Jonathan and Weisstein, Eric W. "Retract." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Retract.html

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