Naslov
Coherent inverse systems and strong shape theory

Autori
Mardešić, Sibe ; Šekutkovski, N.

Izvornik
Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti (1845-4100) 8 (1989), 444; 63-73

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

Ključne riječi
strong shape ; coherent prohomotopy category ; ANR-resolutions ; inverse systems

Sažetak
The first author and Yu. T. Lisitsa have developed a strong (fine) shape theory for arbitrary topological spaces which is based on an explicitly constructed coherent prohomotopy category of order ∞ by making use of ANR-resolutions of spaces in order to relate spaces with inverse systems and define the strong shape of a space. The resolutions turned out to be useful in the non-compact case, while in the compact case they coincide with inverse limits. In the paper under review the authors have extended the theory to the case of coherent inverse systems, i.e. inverse systems where the commutativity of bonding maps holds only up to homotopies, which themselves commute up to higher order homotopies of all orders. Again, the ANR-resolutions of spaces are used as a device for passing from spaces to coherent inverse systems and defining the strong shape. We omit descriptions of involved notions because of their technical complexity.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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