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Strong Deformation Retract


A subspace A of X is called a strong deformation retract of X if there is a homotopy F:X×I->X (called a retract) such that for all x in X, a in A, and t in I,

1. F(x,0)=x,

2. F(x,1) in A, and

3. F(a,t)=a.

If the last equation is required only for t=1, the retract is called simply a deformation retract.


See also

Deformation, Deformation Retract, Retract

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References

Bredon, G. E. Topology and Geometry. New York: Springer-Verlag, 1993.Hatcher, A. Algebraic Topology. Cambridge, England: Cambridge University Press, 2001.

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Strong Deformation Retract

Cite this as:

Weisstein, Eric W. "Strong Deformation Retract." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StrongDeformationRetract.html

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