Naslov
A Note on Finite Coarse Shape Groups

Autori
Jelić, Ivan ; Koceić-Bilan, Nikola

Izvornik
Axioms (2075-1680) 12 (2023), 4; 377, 12

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

Ključne riječi
topological space ; inverse system ; pro-category ; pro*-category ; shape ; finite coarse shape ; coarse shape ; shape group ; polyhedron ; exactness

Sažetak
In this paper, we investigate properties concerning some recently introduced finite coarse shape invariants—the k-th finite coarse shape group of a pointed topological space and the k-th relative finite coarse shape group of a pointed topological pair. We define the notion of finite coarse shape group sequence of a pointed topological pair (X, X0, x0) as an analogue of homotopy and (coarse) shape group sequences and show that for any pointed topological pair, the corresponding finite coarse shape group sequence is a chain. On the other hand, we construct an example of a pointed pair of metric continua whose finite coarse shape group sequence fails to be exact. Finally, using the aforementioned pair of metric continua together with a pointed dyadic solenoid, we show that finite coarse-shape groups, in general, differ from both shape and coarse-shape groups

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA