Shape theory intrinsically.

Zvonko Cerin

Publicacions Matemàtiques (1993)

  • Volume: 37, Issue: 2, page 317-334
  • ISSN: 0214-1493

Abstract

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We prove in this paper that the category HM whose objects are topological spaces and whose morphisms are homotopy classes of multi-nets is naturally equivalent to the shape theory Sh. The description of the category HM was given earlier in the article "Shape via multi-nets". We have shown there that HM is naturally equivalent to Sh only on a rather restricted class of spaces. This class includes all compact metric spaces where a similar intrinsic description of the shape category using multi-valued functions was given by José M. R. Sanjurjo in [5] and [6].

How to cite

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Cerin, Zvonko. "Shape theory intrinsically.." Publicacions Matemàtiques 37.2 (1993): 317-334. <http://eudml.org/doc/41429>.

@article{Cerin1993,
abstract = {We prove in this paper that the category HM whose objects are topological spaces and whose morphisms are homotopy classes of multi-nets is naturally equivalent to the shape theory Sh. The description of the category HM was given earlier in the article "Shape via multi-nets". We have shown there that HM is naturally equivalent to Sh only on a rather restricted class of spaces. This class includes all compact metric spaces where a similar intrinsic description of the shape category using multi-valued functions was given by José M. R. Sanjurjo in [5] and [6].},
author = {Cerin, Zvonko},
journal = {Publicacions Matemàtiques},
keywords = {Teoría de la forma; Categorías; Espacios topológicos; Clases de homotopía; Functores; multi-net; multivalued maps; shape of metric compacta; homotopy theory of normal covers; multivalued functions},
language = {eng},
number = {2},
pages = {317-334},
title = {Shape theory intrinsically.},
url = {http://eudml.org/doc/41429},
volume = {37},
year = {1993},
}

TY - JOUR
AU - Cerin, Zvonko
TI - Shape theory intrinsically.
JO - Publicacions Matemàtiques
PY - 1993
VL - 37
IS - 2
SP - 317
EP - 334
AB - We prove in this paper that the category HM whose objects are topological spaces and whose morphisms are homotopy classes of multi-nets is naturally equivalent to the shape theory Sh. The description of the category HM was given earlier in the article "Shape via multi-nets". We have shown there that HM is naturally equivalent to Sh only on a rather restricted class of spaces. This class includes all compact metric spaces where a similar intrinsic description of the shape category using multi-valued functions was given by José M. R. Sanjurjo in [5] and [6].
LA - eng
KW - Teoría de la forma; Categorías; Espacios topológicos; Clases de homotopía; Functores; multi-net; multivalued maps; shape of metric compacta; homotopy theory of normal covers; multivalued functions
UR - http://eudml.org/doc/41429
ER -

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