Continuous linear extension of functions

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

Research output: Contribution to journalArticlepeer-review

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

Keywords

  • Continuous linear operator
  • Extension of functions
  • Metric space

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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