%0 Journal Article
%A Rodríguez Sanjurjo, José Manuel
%T On mutational deformation retracts
%D 1989
%@ 0009-725X
%U https://hdl.handle.net/20.500.14352/58579
%X In ANR theory, the following result is well known: Suppose that X ′   is an ANR and X  is a subspace of X ′  . Then X  is a strong (or stationary) deformation retract of X ′   if and only if X  is a deformation retract of X ′  . In this paper, a generalization of this result is obtained in Fox shape theory: Let r:U(X ′ ,P)→U(X,P)  be a deformation mutational retraction. Then r  is stationary if and only if r  is regular, where a mutational retraction r:U(X ′ ,P)→U(X,P)  is regular if for every U ′ ∈U(X ′ ,P)  and for every r,r ′ ∈r  with range U ′  , there is V ′ ∈U(X ′ ,P)  such that r∣ ∣ V ′ ≃r ′ ∣ ∣ V ′   (rel. X ) in U ′  .
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