Topological coarse shape groups of compact metric spaces (CROSBI ID 241947)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Koceić-Bilan, Nikola ; Čuka, Zdravko
engleski
Topological coarse shape groups of compact metric spaces
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.
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
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Podaci o izdanju
21 (532)
2017.
205-217
objavljeno
1845-4100
1849-2215
10.21857/9xn31cvr1y
Povezanost rada
Matematika