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Let X be a space and let A and B be subspaces of X
with
. Then A is called a deformation retract of B
over
X provided that the identity mapping
is homotopic in X to
a retraction
. Further, A is called a
strong deformation retract of B over X provided that it is a deformation
retract of B over X and the homotopy keeps the points of A fixed
throughout the entire deformation of B into A (see e.g.
[41, Definition 6.3, p. 324]).
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-02-21