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Let be a space and let and be subspaces of
with
. Then is called a *deformation retract of*
over
provided that the identity mapping
is homotopic in to
a retraction
. Further, is called a
*strong deformation retract of* over provided that it is a deformation
retract of over and the homotopy keeps the points of fixed
throughout the entire deformation of into (see e.g.
[Dugundji 1966, Definition 6.3, p. 324]).

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*Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih*

*2001-11-30*