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$%Čerin, Shape theory of maps, Rev. Mat. Univ. Complut. Madrid 8 (1995), no. 1, 121–154.%$
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
. The category
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.
1991 Mathematics Subject Classification: 54B25, 54F45, 54C56.