engleski

A category whose isomorphisms induce an equivalence relation coarser than shape

Let Sh denote the usual shape category of metric compacta. In the paper one defines a new category S*, whose objects are all metric compacta, and one defines a functor Sh->S*, which preserves objects. In shape fibration of metric continuum fiers need not have the same shape, but they are isomorphic objects in S*. Various shape invariant classes of compacta, like FANR's and movable continua, are also S*- equivalent classes. Compact ANR's are isomorphic in S* if and only if they have the same homotopy type.

shape ; S-equivalence ; shape fibration

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