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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On simultaneous linear extensions of partial (pseudo)metrics


Authors: E. D. Tymchatyn and M. Zarichnyi
Journal: Proc. Amer. Math. Soc. 132 (2004), 2799-2807
MSC (2000): Primary 54E35, 54C20, 54E40
Published electronically: April 21, 2004
MathSciNet review: 2054807
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the question of simultaneous extension of (pseudo) metrics defined on nonempty closed subsets of a compact metrizable space. The main result is a counterpart of the result due to Künzi and Shapiro for the case of extension operators of partial continuous functions and includes, as a special case, Banakh's theorem on linear regular operators extending (pseudo)metrics.


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Additional Information

E. D. Tymchatyn
Affiliation: Department of Mathematics and Statistics, University of Saskatchewan, Room 142 McLean Hall, 106 Wiggins Road, Saskatoon, Saskatchewan, Canada S7N 5E6
Email: tymchat@math.usask.ca

M. Zarichnyi
Affiliation: Department of Mechanics and Mathematics, Lviv National University, Universytetska 1, 79000 Lviv, Ukraine
Email: topos@franko.lviv.ua, mzar@litech.lviv.ua

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07413-1
PII: S 0002-9939(04)07413-1
Received by editor(s): November 18, 2002
Received by editor(s) in revised form: May 29, 2003
Published electronically: April 21, 2004
Additional Notes: The paper was finished during the second named author’s visit to the University of Saskatchewan. This research was supported in part by NSERC research grant OGP 005616
Communicated by: Alan Dow
Article copyright: © Copyright 2004 American Mathematical Society