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].
@article{urn:eudml:doc:41429,
title = {Shape theory intrinsically.},
journal = {Publicacions Matem\`atiques},
volume = {37},
year = {1993},
pages = {317-334},
mrnumber = {MR1249234},
zbl = {0808.54014},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41429}
}
Cerin, Zvonko. Shape theory intrinsically.. Publicacions Matemàtiques, Tome 37 (1993) pp. 317-334. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41429/