Resumen:
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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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