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On mutational deformation retracts



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Rodríguez Sanjurjo, José Manuel (1989) On mutational deformation retracts. Rendiconti del Circolo Matematico di Palermo, 21 (Supple). pp. 291-293. ISSN 0009-725X

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Official URL: http://dml.cz/bitstream/handle/10338.dmlcz/701449/WSGP_08-1988-1_21.pdf


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 ′ .

Item Type:Article
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Proceedings of the Winter School on Geometry and Physics (Srní, 1988).

Uncontrolled Keywords:MANR-spaces; W-shape deformation retract; Fox shape theory; regular mutational retraction; deformation mutational retraction
Subjects:Sciences > Mathematics > Topology
ID Code:21941
Deposited On:19 Jun 2013 16:37
Last Modified:12 Dec 2018 15:13

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