On quasi-metric and metric spaces
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- by Maciej Paluszyński and Krzysztof Stempak
- Proc. Amer. Math. Soc. 137 (2009), 4307-4312
- DOI: https://doi.org/10.1090/S0002-9939-09-10058-8
- Published electronically: August 7, 2009
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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 $0<p\le 1$, 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.References
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Bibliographic Information
- Maciej Paluszyński
- Affiliation: Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50–384 Wrocław, Poland
- Email: mpal@math.uni.wroc.pl
- 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
- Email: Krzysztof.Stempak@pwr.wroc.pl
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 4307-4312
- MSC (2000): Primary 54E35; Secondary 54E15
- DOI: https://doi.org/10.1090/S0002-9939-09-10058-8
- MathSciNet review: 2538591