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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a complete metric space. We prove that there is a continuous, linear, regular extension operator from the space of all partial, continuous, real-valued, bounded functions with closed, bounded domains in to the space of all continuous, bounded, real-valued functions on 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:
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

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

DOI:
https://doi.org/10.1090/S0002-9939-2010-10424-0

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