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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Continuous linear extension of functions
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by A. Koyama, I. Stasyuk, E. D. Tymchatyn and A. Zagorodnyuk PDF
Proc. Amer. Math. Soc. 138 (2010), 4149-4155 Request permission


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
  • Email:
  • 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
  • Email:
  • E. D. Tymchatyn
  • Affiliation: Department of Mathematics and Statistics, University of Saskatchewan, McLean Hall, 106 Wiggins Road, Saskatoon, SK S7N 5E6, Canada
  • MR Author ID: 175580
  • Email:
  • 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
  • Email:
  • 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
  • © Copyright 2010 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 4149-4155
  • MSC (2010): Primary 54C20, 54C30; Secondary 54E40
  • DOI:
  • MathSciNet review: 2679637