| Autor: |
Ivan Jelić, Nikola Koceić-Bilan |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
Axioms, Vol 12, Iss 4, p 377 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2075-1680 |
| DOI: |
10.3390/axioms12040377 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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