Continuous linear extension of functions

Akira Koyama, I. Stasyuk, E. D. Tymchatyn, A. Zagorodnyuk

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)4149-4155
Number of pages7
JournalProceedings of the American Mathematical Society
Volume138
Issue number11
DOIs
Publication statusPublished - 2010 Nov
Externally publishedYes

Fingerprint

Continuous Extension
Linear Extension
Configuration Space
Regular Operator
Extension Operator
Complete Metric Space
Uniform convergence
Compact Set
Bounded Domain
Continuous Function
Topology
Partial
Closed

Keywords

  • Continuous linear operator
  • Extension of functions
  • Metric space

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Continuous linear extension of functions. / Koyama, Akira; Stasyuk, I.; Tymchatyn, E. D.; Zagorodnyuk, A.

In: Proceedings of the American Mathematical Society, Vol. 138, No. 11, 11.2010, p. 4149-4155.

Research output: Contribution to journalArticle

Koyama, Akira ; Stasyuk, I. ; Tymchatyn, E. D. ; Zagorodnyuk, A. / Continuous linear extension of functions. In: Proceedings of the American Mathematical Society. 2010 ; Vol. 138, No. 11. pp. 4149-4155.
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