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
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.References
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Additional Information
- A. Koyama
- Affiliation: Faculty of Science, Shizuoka University, 836 Ohya 422-8059, Shizuoka, Japan
- Email: sakoyam@ipc.shizuoka.ac.jp
- 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: i_stasyuk@yahoo.com
- 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: tymchat@math.usask.ca
- 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: andriyzag@yahoo.com
- 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: https://doi.org/10.1090/S0002-9939-2010-10424-0
- MathSciNet review: 2679637