Original scientific paper

https://doi.org/10.3336/gm.42.1.12

The coarse shape

Nikola Koceić Bilan orcid.org/0000-0003-4430-0091 ; Department of Mathematics, University of Split, Teslina 12/III, 21000 Split, Croatia
Nikica Uglešić ; 23287 Veli Rat, Dugi Otok, Croatia

Abstract

Given a category C, a certain category pro*-C on inverse systems in C is constructed, such that the usual pro-category pro-C may be considered as a subcategory of pro*-C. By simulating the (abstract) shape category construction, Sh(C, D), an (abstract) coarse shape category Sh*(C, D) is obtained. An appropriate functor of the shape category to the coarse shape category exists. In the case of topological spaces, C = HTop and D = HPol or D = HANR, he corresponding realizing category for Sh* is pro*-HPol or pro*-HANR respectively. Concerning an operative characterization of a coarse shape isomorphism, a full analogue of the well known Morita lemma is proved, while in the case of inverse sequences, a useful sufficient condition is established. It is proved by examples that for C = Grp (groups) and C = HTop, the classification of inverse systems in pro*-C is strictly coarser than in pro-C. Therefore, the underlying coarse shape theory for topological spaces makes sense.

Keywords

Topological space; compactum; polyhedron; ANR; category; homotopy; shape; S*-equivalence

Hrčak ID:

12892

URI

https://hrcak.srce.hr/12892

Publication date:

12.6.2007.

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