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Proceedings of the American Mathematical Society

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Continuous linear extension of functions

Authors: A. Koyama, I. Stasyuk, E. D. Tymchatyn and A. Zagorodnyuk
Journal: Proc. Amer. Math. Soc. 138 (2010), 4149-4155
MSC (2010): Primary 54C20, 54C30; Secondary 54E40
Published electronically: May 26, 2010
MathSciNet review: 2679637
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Abstract: Let $ (X,d)$ be a complete metric space. We prove that there is a continuous, linear, regular extension operator from the space $ C^*_b$ of all partial, continuous, real-valued, bounded functions with closed, bounded domains in $ X$ to the space $ C^*(X)$ of all continuous, bounded, real-valued functions on $ X$ with the topology of uniform convergence on compact sets. This is a variant of a result of Kunzi and Shapiro for continuous functions with compact, variable domains.

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Additional Information

A. Koyama
Affiliation: Faculty of Science, Shizuoka University, 836 Ohya 422-8059, Shizuoka, Japan

I. Stasyuk
Affiliation: Department of Mechanics and Mathematics, Lviv National University, Universytetska St. 1, Lviv 79000, Ukraine
Address at time of publication: Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, Box 5002, North Bay, ON, P1B 8L7, Canada

E. D. Tymchatyn
Affiliation: Department of Mathematics and Statistics, University of Saskatchewan, McLean Hall, 106 Wiggins Road, Saskatoon, SK S7N 5E6, Canada

A. Zagorodnyuk
Affiliation: Institute for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, 3b Naukova St., Lviv 79060, Ukraine
Address at time of publication: Prycarpathian National University, Ivano-Frankivsk, Ukraine

Keywords: Extension of functions, continuous linear operator, metric space
Received by editor(s): September 10, 2009
Received by editor(s) in revised form: November 20, 2009, and February 3, 2010
Published electronically: May 26, 2010
Additional Notes: The second, third, and fourth authors were supported in part by NSERC grant No. OGP 0005616
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2010 American Mathematical Society

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