Translator Disclaimer
2015 Optimal Quasi-Metrics in a Given Pointwise Equivalence Class do not Always Exist
Dan Brigham, Marius Mitrea
Publ. Mat. 59(2): 479-509 (2015).

Abstract

In this paper we provide an answer to a question found in "Groupoid metrization theory," With applications to analysis on quasi-metric spaces and functional analysis,, namely when given a quasi-metric $\rho$, if one examines all quasi-metrics which are pointwise equivalent to $\rho$, 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.

Citation

Download Citation

Dan Brigham. Marius Mitrea. "Optimal Quasi-Metrics in a Given Pointwise Equivalence Class do not Always Exist." Publ. Mat. 59 (2) 479 - 509, 2015.

Information

Published: 2015
First available in Project Euclid: 30 July 2015

zbMATH: 1351.46023
MathSciNet: MR3374615

Subjects:
Primary: 46E30, 52A07
Secondary: 46A16, 46A80, 54E35, ‎54E50‎

Rights: Copyright © 2015 Universitat Autònoma de Barcelona, Departament de Matemàtiques

JOURNAL ARTICLE
31 PAGES


SHARE
Vol.59 • No. 2 • 2015
Back to Top