# Classifications coarser than shape - Mathematical Communications, Vol.13 No.2 December 2008.

Classifications coarser than shape - Mathematical Communications, Vol.13 No.2 December 2008. - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Mathematical Communications, Vol.13 No.2 December 2008. -

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.

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