Fiberwise shape theory.
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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...
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