Ultrametrics on Čech homology groups
This paper is devoted to introducing additional structure on Čech homology groups. First, we redefine the Čech homology groups in terms of what we have called approximative homology by using approximative sequences of cycles, just as Borsuk introduced shape groups using approximative maps. From this...
| Authors: | , , |
|---|---|
| Format: | article |
| Publication Date: | 2019 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | Spanish |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/13191 |
| Online Access: | https://hdl.handle.net/20.500.14352/13191 |
| Access Level: | Open access |
| Keyword: | 515.14 Čech homology Čech homology groups Approximative cycle and boundary Approximative homology Ultrametric Grupos (Matemáticas) Topología 1210 Topología |
| Summary: | This paper is devoted to introducing additional structure on Čech homology groups. First, we redefine the Čech homology groups in terms of what we have called approximative homology by using approximative sequences of cycles, just as Borsuk introduced shape groups using approximative maps. From this point on, we are able to construct complete ultrametrics on Čech homology groups. The uniform type (and then the group topology) generated by the ultrametric leads to a shape invariant which we use to deduce topological consequences. |
|---|