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**Petrakis, Iosif (2020): MCSHANE-WHITNEY EXTENSIONS IN CONSTRUCTIVE ANALYSIS. In: Logical Methods in Computer Science, Vol. 16, No. 1, 18**

**Full text not available from 'Open Access LMU'.**

## Abstract

Within Bishop-style constructive mathematics we study the classical McShane-Whitney theorem on the extendability of real-valued Lipschitz functions defined on a subset of a metric space. Using a formulation similar to the formulation of McShane-Whitney theorem, we show that the Lipschitz real-valued functions on a totally bounded space are uniformly dense in the set of uniformly continuous functions. Through the introduced notion of a McShane-Whitney pair we describe the constructive content of the original McShane-Whitney extension and we examine how the properties of a Lipschitz function defined on the subspace of the pair extend to its McShane-Whitney extensions on the space of the pair. Similar McShane-Whitney pairs and extensions are established for Holder functions and nu-continuous functions, where nu is a modulus of continuity. A Lipschitz version of a fundamental corollary of the Hahn-Banach theorem, and the approximate McShane-Whitney theorem are shown.

Item Type: | Journal article |
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Faculties: | Mathematics, Computer Science and Statistics > Mathematics |

Subjects: | 500 Science > 510 Mathematics |

ISSN: | 1860-5974 |

Language: | English |

Item ID: | 88970 |

Date Deposited: | 25. Jan 2022, 09:28 |

Last Modified: | 25. Jan 2022, 09:28 |