Contraction of a Generalized Metric Structure
| dc.creator | Wallet, Guy | |
| dc.date | 2008-12-10 | |
| dc.date.accessioned | 2026-07-07T12:11:39Z | |
| dc.date.available | 2026-07-07T12:11:39Z | |
| dc.description | In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we introduce a new metric structure - the galactic spaces - which depends on an ordered field extension of R. Moreover, some natural transformations of the category of galactic spaces, the contractions, are of particular interest: they generalize usual homotheties, they have a ratio which may be an infinitesimal, they are able to modify the topology and they satisfy a nice composition rule. With the help of nonstandard extensions we can associate to any metric space an infinite family of galactic spaces; lastly, we study some limit properties of this family. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/0812.1898 | |
| dc.identifier | http://arxiv.org/abs/0812.1898 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210289 | |
| dc.subject | Geometric Topology | |
| dc.subject | Metric Geometry | |
| dc.subject | 03H05, 12J15, 26E35, 54E35 | |
| dc.title | Contraction of a Generalized Metric Structure | |
| dc.type | text |