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.
@article{urn:eudml:doc:44182,
title = {Shape theory of maps.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {8},
year = {1995},
pages = {121-154},
zbl = {0870.54020},
mrnumber = {MR1356439},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44182}
}
Cerin, Zvonko. Shape theory of maps.. Revista Matemática de la Universidad Complutense de Madrid, Tome 8 (1995) pp. 121-154. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44182/