Original scientific paper

A subshape spectrum for compacta

Nikica Uglešić
Branko Červar

Abstract

A sequence of categories and functors between them are constructed. They form a subshape spectrum for compacta in the following sense: Each of these categories classifies compact ANR's just as the homotopy category does; the classification of compacta by the "finest" of these categories coincides with the shape type classification; moreover, the finest category contains a subcategory which is isomorphic to the shape category; 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.

Further, a few applications of the "subshape spectrum theory" are demonstrated. It is shown that the S*-equivalence (a uniformization of the Mardesic S-equivalence) and the q*-equivalence (a uniformization of the Borsuk quasi-equivalence) admit the category characterizations within the subshape spectrum, and that the q*-equivalence implies (but is not equivalent to) the S*-equivalence.

Keywords

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

Hrčak ID:

386

URI

https://hrcak.srce.hr/386

Publication date:

9.11.2005.

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