On limits of shape maps

Sanjurjo, José Manuel Rodríguez

doi:10.1016/0166-8641(86)90039-8

Cited by 4 publications

(3 citation statements)

References 8 publications

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“…In order to prove this result we must first give a new characterization of internally movable compacta in terms of multivalued maps. In a forthcoming paper we shall give similar characterizations of the most usual concepts of the theory of shape and also of the notions related to the limits of shape maps considered in [19].…”

Section: Multi-nets and Internally Movable Compactamentioning

confidence: 98%

An intrinsic description of shape

Sanjurjo¹

1992

Trans. Amer. Math. Soc.

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We give in this paper a description of the shape category of compacta in terms of multivalued maps. We introduce the notion of a multi-net and prove that the shape category of compacta is isomorphic to the category HN whose objects are metric compacta and whose morphisms are homotopy classes of multi-nets. This description is intrinsic in the sense that it does not make use of external elements such as ANR-expansions or embeddings in appropriate AR-spaces. We present many applications of this new formulation of shape.

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Section: Multi-nets and Internally Movable Compactamentioning

confidence: 98%

An intrinsic description of shape

Sanjurjo¹

1992

Trans. Amer. Math. Soc.

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“…

CECH SPACES OF LOOPS 331 establish a connection with the theory of dynamical systems and, in particular, with properties of asymptotically stable attractors.Other results about relationships between shape theory and the theory of multivalued maps appear in [6,14,15,18,25,28]. In a forthcoming paper we shall study further connections with the notions related to the limits of shape maps considered in [24]. The reader is referred to the texts by Borsuk [5], Cordier and Porter [7], Dydak and Segal [9], Mardesic and Segal [19] and the lists of problems [10] and [30] for information about shape theory.

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confidence: 93%

Multihomotopy, Čech Spaces of loops and Shape Groups

Sanjurjo

1994

Proceedings of the London Mathematical Society

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“…An approximative map f={f k ,X -+ Y} is said to be accessible [11] provided for every c>0 and every neigh- Let n be a positive integer . We say that the shape category (see [2], [4], [12]) of the approximative map f= ={fk ,X -_> Y} is less or equal than n if for every neigh borhaod Y of Y in Q, X -can be expressed as a union of sub_compacta X 1 , .…”

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confidence: 99%