Naslov
The S_n-equivalence of compacta

Autori
Červar, Branko ; Uglešić Nikica

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
International Conference and Workshop on Geometric Topology honoring Karol Borsuk's life and work on the 100th anniversary of his birth / - , 2005

Skup
International Conference and Workshop on Geometric Topology honoring Karol Borsuk's life and work on the 100th anniversary of his birth

Mjesto i datum
Będlewo, Poljska, 03.06.2005. - 10.06.2005

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Compactum; ANR; shape; S-equivalece

Sažetak
By reducing the Mardešić S-equivalence to a finite case, i.e. to each n∈ {;0};∪ N separately, we have derived the notions of S_{;n};-equivalence and S_{;n+1};-domination of compacta. The S_{;n};-equivalence for all n coincides with the S-equivalence. Further, the S_{;n+1};-equivalence implies S_{;n+1};-domination, and the S_{;n+1};-domination implies S_{;n};-equivalence. The S₀ -equivalence is a trivial equivalence relation, i.e. all non empty compacta are mutually S₀ -equivalent. It is proved that the S₁ -equivalence is strictly finer than the S₀ -equivalence, and that the S₂ -equivalence is strictly finer than the S₁ -equivalence. Thus, the S₁ -equivalence is strictly coarser than the S-equivalence. Further, the S₁ -equivalence classifies compacta which are homotopy (shape) equivalent to ANR's up to the homotopy types (shape types). The S₂ -equivalence class of an FANR coincides with its S-equivalence class as well as with its shape type class. Finally, it is conjectured that, for every n, there exists an n′ >n such that the S_{;n′ };-equivalence is strictly finer than the S_{;n};-equivalence.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA