### 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 language | English |
---|---|

Pages (from-to) | 4149-4155 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 138 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2010 Nov |

Externally published | Yes |

### Fingerprint

### Keywords

- Continuous linear operator
- Extension of functions
- Metric space

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*138*(11), 4149-4155. https://doi.org/10.1090/S0002-9939-2010-10424-0

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

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 138, no. 11, pp. 4149-4155. https://doi.org/10.1090/S0002-9939-2010-10424-0

}

TY - JOUR

T1 - Continuous linear extension of functions

AU - Koyama, Akira

AU - Stasyuk, I.

AU - Tymchatyn, E. D.

AU - Zagorodnyuk, A.

PY - 2010/11

Y1 - 2010/11

N2 - 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.

AB - 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.

KW - Continuous linear operator

KW - Extension of functions

KW - Metric space

UR - http://www.scopus.com/inward/record.url?scp=78149233154&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78149233154&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2010-10424-0

DO - 10.1090/S0002-9939-2010-10424-0

M3 - Article

AN - SCOPUS:78149233154

VL - 138

SP - 4149

EP - 4155

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 11

ER -