Optimal quasi-metrics in a given pointwise equivalence class do not always exist
In this paper we provide an answer to a question found in [3], namely when given a quasi-metric p, if one examines all quasi-metrics which are pointwise equivalent to p, does there exist one which is most like an ultrametric (or, equivalently, exhibits an optimal amount of Hölder regularity)? The an...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:133144 |
| Acceso en línea: | https://ddd.uab.cat/record/133144 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_59215_08 |
| Access Level: | acceso abierto |
| Palabra clave: | F-norm Holder regularity Minkowski functional Metrization theorem Metrizing quasi-modular Modulus of concavity Quasi-metric, quasi-norm Rolewicz-orlicz space Topological vector space |
| Sumario: | In this paper we provide an answer to a question found in [3], namely when given a quasi-metric p, if one examines all quasi-metrics which are pointwise equivalent to p, does there exist one which is most like an ultrametric (or, equivalently, exhibits an optimal amount of Hölder regularity)? The answer, in general, is negative, which we demonstrate by constructing a suitable Rolewicz-Orlicz space. |
|---|