On continuous linear operators extending metrics

Authors:
I. Stasyuk and E. D. Tymchatyn

Journal:
Proc. Amer. Math. Soc. **141** (2013), 2913-2921

MSC (2010):
Primary 54C20, 54C30; Secondary 54E40

Published electronically:
April 24, 2013

MathSciNet review:
3056581

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Abstract: Let be a complete metric space. We prove that there is a continuous, linear extension operator from the space of all partial, continuous, bounded metrics with closed, bounded domains in endowed with the Hausdorff metric topology to the space of all continuous, bounded, metrics on with the topology of uniform convergence on compact sets. This is a variant of the result of Tymchatyn and Zarichnyi for continuous metrics defined on closed, variable domains in a compact metric space. We get a similar result for the case of continuous real-valued functions.

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Additional Information

**I. Stasyuk**

Affiliation:
Department of Mechanics and Mathematics, Lviv National University, Universytetska Str. 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, 51B 8L7, Canada

Email:
i$\textunderscore$stasyuk@yahoo.com

**E. D. Tymchatyn**

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

Email:
tymchat@math.usask.ca

DOI:
https://doi.org/10.1090/S0002-9939-2013-11547-9

Keywords:
Extension of metrics,
continuous linear operator,
metric space

Received by editor(s):
October 14, 2010

Received by editor(s) in revised form:
November 8, 2011

Published electronically:
April 24, 2013

Additional Notes:
The authors were supported in part by NSERC grant No. OGP 0005616

Communicated by:
Alexander N. Dranishnikov

Article copyright:
© Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.