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Optimal quasi-metrics in a given pointwise equivalence class do not always exist
Brigham, Dan (University of Missouri at Columbia. Department of Mathematics)
Mitrea, Marius (University of Missouri at Columbia. Department of Mathematics)

Data: 2015
Resum: 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.
Drets: Tots els drets reservats
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Matèria: F-norm ; Holder regularity ; Minkowski functional ; Metrization theorem ; Metrizing quasi-modular ; Modulus of concavity ; Quasi-metric, quasi-norm ; Rolewicz-orlicz space ; Topological vector space
Publicat a: Publicacions matemàtiques, Vol. 59 Núm. 2 (2015) , p. 479–509 (Articles) , ISSN 2014-4350

Adreça original:
DOI: 10.5565/PUBLMAT_59215_08

31 p, 452.5 KB

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