Original scientific paper

Classifications coarser than shape

Nikica Uglešić ; University of Zadar, Zadar, Croatia

Abstract

About thirty years ago, in the time of an intensive study of the shape
theory, several classifications of metric compacta coarser than shape were introduced. Two of them have been of a special interest: The
quasi-equivalence (K. Borsuk, 1976) and S-equivalence (S. Mardešić, 1978).
In the last decade a much deeper view into these relations has been
achieved. In attempt to characterize or, at least, describe them in a
category framework on purpose of easier operative studying, several new classifications and new "shape" theories occurred. The most interesting among them are the coarse and weak shape theory. This paper is intended to be an exhaustive survey of new classifications and corresponding theories, their mutual relations and the most important results.

Keywords

shape; quasi-equivalence; $\overline{q}$-equivalence; S-equivalence; $S^{\ast }$-equivalence; $S_{n}$-equivalence; coarse shape; weak shape

Hrčak ID:

30886

URI

https://hrcak.srce.hr/30886

Publication date:

23.12.2008.

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