Shape theory of maps.

Zvonko Cerin

Revista Matemática de la Universidad Complutense de Madrid (1995)

  • Volume: 8, Issue: 1, page 121-154
  • ISSN: 1139-1138

Abstract

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We shall describe a modification of homotopy theory of maps which we call shape theory of maps. This is accomplished by constructing the shape category of maps HMb. The category HMb is built using multi-valued functions. Its objects are maps of topological spaces while its morphisms are homotopy classes of collections of pairs of multi-valued functions which we call multi-binets. Various authors have previously given other descriptions of shape categories of maps. Our description is intrinsic in the sense that we do not use any outside objects. It is a version of the author?s extension to arbitrary topological spaces of Sanjurjo?s approach to shape theory via small multi-valued functions adapted to maps.

How to cite

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Cerin, Zvonko. "Shape theory of maps.." Revista Matemática de la Universidad Complutense de Madrid 8.1 (1995): 121-154. <http://eudml.org/doc/44182>.

@article{Cerin1995,
abstract = {We shall describe a modification of homotopy theory of maps which we call shape theory of maps. This is accomplished by constructing the shape category of maps HMb. The category HMb is built using multi-valued functions. Its objects are maps of topological spaces while its morphisms are homotopy classes of collections of pairs of multi-valued functions which we call multi-binets. Various authors have previously given other descriptions of shape categories of maps. Our description is intrinsic in the sense that we do not use any outside objects. It is a version of the author?s extension to arbitrary topological spaces of Sanjurjo?s approach to shape theory via small multi-valued functions adapted to maps.},
author = {Cerin, Zvonko},
journal = {Revista Matemática de la Universidad Complutense de Madrid},
keywords = {Clases de homotopía; Grupos duales de homotopía; Mapas; Teoría de la forma; Espacios topológicos; multi-binet; bihomotopy; bishape equivalence; shape theory for maps; shape category of maps},
language = {eng},
number = {1},
pages = {121-154},
title = {Shape theory of maps.},
url = {http://eudml.org/doc/44182},
volume = {8},
year = {1995},
}

TY - JOUR
AU - Cerin, Zvonko
TI - Shape theory of maps.
JO - Revista Matemática de la Universidad Complutense de Madrid
PY - 1995
VL - 8
IS - 1
SP - 121
EP - 154
AB - We shall describe a modification of homotopy theory of maps which we call shape theory of maps. This is accomplished by constructing the shape category of maps HMb. The category HMb is built using multi-valued functions. Its objects are maps of topological spaces while its morphisms are homotopy classes of collections of pairs of multi-valued functions which we call multi-binets. Various authors have previously given other descriptions of shape categories of maps. Our description is intrinsic in the sense that we do not use any outside objects. It is a version of the author?s extension to arbitrary topological spaces of Sanjurjo?s approach to shape theory via small multi-valued functions adapted to maps.
LA - eng
KW - Clases de homotopía; Grupos duales de homotopía; Mapas; Teoría de la forma; Espacios topológicos; multi-binet; bihomotopy; bishape equivalence; shape theory for maps; shape category of maps
UR - http://eudml.org/doc/44182
ER -

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