Strong Deformation Retract

A subspace  of  is called a strong deformation retract of  if there is a homotopy  (called a retract) such that for all , , and ,

1. ,

2. , and

3. .

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

REFERENCES:

Bredon, G. E. Topology and Geometry. New York: Springer-Verlag, 1993.

Hatcher, A. Algebraic Topology. Cambridge, England: Cambridge University Press, 2001.