Resumen de Fiberwise shape theory
Zvonko Cerin
We shall describe a modification of fiberwise homotopy theory which we call fiberwise shape theory. This is accomplished by constructing the fiberwise shape category $\mathcal{F}s_B$. The category $\mathcal{F}s_B$ is built using multi-valued functions. Its objects are fiberwise topological spaces while its morphisms are fiberwise homotopy classes of collections of multi-valued functions which we call fiberwise multi-nets. When $B$ is a single-element space, the fiberwise shape category is isomorphic with the shape category. Various authors have previously given other descriptions of fiberwise shape categories under additional assumptions. Our description is intrinsic in the sense that we do not use any outside objects. It is a fiberwise version of the author’s extension to arbitrary topological spaces of Sanjurjo’s approach to shape theory via small multi-valued functions.
