engleski

The Uniform Shape Spectrum for Compacta

The countable families of categories and functors are constructed such that they may represent a "uniform shape spectrum" for compacta in the following sense: Each of these categories classifies compact ANR's as the homotopy category does ; the classification of compacta by the "finest" of these categories coincides with the shape type classification ; there exists a functor of the shape category to each of these categories, as well as of a "finer" category to a "coarser" one ; the functors commute according to the indices. As an application, it is shown that the S^{;∗ };-equivalence (a uniformization of the Mardešić S-equivalence, [2] i [3]) and the q^{;∗ };-equivalence (a uniformization of the Borsuk quasi-equivalence, [1] i [4]) admit the category characterizations within this uniform shape spectrum, and that q^{;∗ };-equivalence implies S^{;∗ };-equivalence.

compactum; ANR; inverse sequence; limit; shape type; quasi-equivalence; S-equivalence

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