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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]).
Next: dendroid
Up: Definitions
Previous: decomposable
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-11-30