Naslov
Topological coarse shape groups of compact metric spaces

Autori
Koceić-Bilan, Nikola ; Čuka, Zdravko

Izvornik
Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti (1845-4100) 21 (2017), 532; 205-217

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

Ključne riječi
Inverse system ; pro-category ; pro∗-category ; expansion ; shape ; coarse shape ; homotopy pro-group ; shape group ; coarse shape group ; topological shape homotopy group ; coarse shape path connectedness

Sažetak
The shape theory and, relatively new, coarse shape theory are very useful in studying of topological spaces, as well as of the corresponding algebraic invariants, especially, shape and coarse shape groups. By using certain ultrametrics on special sets of pro- and pro∗-morphisms, we topologize those groups when they refer to compact metric spaces and we get topological groups. In the shape case, they are isomorphic to recently constructed topological shape homotopy groups, while in the coarse shape case we get the coarse shape invariants, denoted by ˇπ∗d ∗ k (X, x0). We have proven some important properties of ˇπ∗d ∗ k (X, x0) and provided few interesting examples.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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