The finite coarse shape groups (CROSBI ID 313883)
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Podaci o odgovornosti
Jelić, Ivan ; Koceić-Bilan, Nikola
engleski
The finite coarse shape groups
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.
Topological space ; Inverse system ; Pro-category ; Pro*-category ; Shape ; Finite coarse shape ; Coarse shape ; Shape group ; Polyhedron
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Podaci o izdanju
320
2022.
108243
14
objavljeno
0166-8641
1879-3207
10.1016/j.topol.2022.108243