Naslov
The finite coarse shape groups

Autori
Jelić, Ivan ; Koceić-Bilan, Nikola

Izvornik
Topology and its applications (0166-8641) 320 (2022); 108243, 14

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

Sažetak
In this paper we define a new pointed finite coarse shape invariant -k-th finite coarse shape group of a pointed topological space and compare it with the corresponding shape and coarse shape group. We also define a functor ˇπkfrom the pointed finite coarse shape category Shto the category Grpof all groups (for k=0to the category Setof all pointed sets) associating with every pointed topologicalspace (X, x0)a k-th finite coarse shape group ˇπk(X, x0)and with every finite coarse shape morphism F:(X, x0)→(Y, y0)a homomorphism (a base point preserving function) ˇπk(F):ˇπk(X, x0)→ˇπk(Y, y0). We show that, in a case of a pointed compact polyhedral system, functor ˇπkis continuous, i.e., commutes with the inverse limit. Finally, finite coarse shape groups of some interesting spaces (dyadic solenoid and arbitrary stable pointed space) are calculated.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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