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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

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

## Abstract

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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Additional Information: | 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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