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On quasi-metric and metric spaces

Authors: Maciej Paluszynski and Krzysztof Stempak
Journal: Proc. Amer. Math. Soc. 137 (2009), 4307-4312
MSC (2000): Primary 54E35; Secondary 54E15
Published electronically: August 7, 2009
MathSciNet review: 2538591
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Abstract: Given a space $ X$ with a quasi-metric $ \rho$ it is known that the so-called $ p$-chain approach can be used to produce a metric in $ X$ equivalent to $ \rho^p$ for some $ 0<p\le1$, hence also a quasi-metric $ \tilde{\rho}$ equivalent to $ \rho$ with better properties. We refine this result and obtain an exponent $ p$ which is, in general, optimal.

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Maciej Paluszynski
Affiliation: Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50–384 Wrocław, Poland

Krzysztof Stempak
Affiliation: Instytut Matematyki i Informatyki, Politechnika Wrocławska, Wyb. Wyspiańskiego 27, 50–370 Wrocław, Poland – and – Katedra Matematyki i Zastosowań Informatyki, Politechnika Opolska, ul. Mikołajczyka 5, 45-271 Opole, Poland

Keywords: Quasi-metric, $p$-chain approach.
Received by editor(s): January 18, 2009
Received by editor(s) in revised form: May 12, 2009
Published electronically: August 7, 2009
Additional Notes: The authors’ research was supported in part by grants KBN #1P03A03029 and MNiSW #N201 054 32/4285, respectively.
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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