Naslov
A subshape spectrum for compacta

Autori
Uglešić, Nikica ; Červar, Branko

Izvornik
Glasnik matematički (0017-095X) 40(60) (2005), 2; 347-384

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

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

Sažetak
The countable families of categories and functors are constructed such that they may represent a \emph{; ; subshape 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 ; 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 \textquotedblleft finer\textquotedblright\ category to a \textquotedblleft coarser\textquotedblright\ one ; the functors commute according to the indices. Further, a few applications of this \textquotedblleft subshape spectrum theory\textquotedblright\ are demonstrated. It is shown that the $S^{; ; \ast }; ; $% -equivalence (a uniformization of the Marde\v{; ; s}; ; i\'{; ; c}; ; $S$-equivalence) and the $q^{; ; \ast }; ; $-equivalence (a uniformization of the Borsuk quasi-equivalence) admit the category characterizations within the subshape spectrum, and that the $q^{; ; \ast }; ; $-equivalence strictly implies the $S^{; ; \ast }; ; $-equivalence.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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