Shape theory intrinsically (Q1325602)

In this interesting paper, the author constructs an isomorphism between the category HM whose objects are topological spaces and whose morphisms are homotopy classes of multi-nets and the category Sh. As a consequence, the author obtains an intrinsic characterization of shape for the class of all topological spaces in terms of multivalued maps. This result extends previous results of the reviewer in which the shape of metric compacta was described in a similar intrinsic way. Another contribution in this direction was given by \textit{M. A. Morón} and \textit{F. R. Ruiz del Portal} [Math. Jap. 39, No. 3, 489-500 (1994; see the review below)] in the case of paracompacta. In order to achieve his results the author develops an elaborate homotopy theory of normal covers and multivalued functions in the class of all topological spaces.