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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

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Volume 24, Issue 2


Chebyshev Distance

Roland Coghetto
Published Online: 2016-12-08 | DOI: https://doi.org/10.1515/forma-2016-0010


In [21], Marco Riccardi formalized that ℝN-basis n is a basis (in the algebraic sense defined in [26]) of Tn and in [20] he has formalized that Tn is second-countable, we build (in the topological sense defined in [23]) a denumerable base of Tn.

Then we introduce the n-dimensional intervals (interval in n-dimensional Euclidean space, pavé (borné) den [16], semi-intervalle (borné) den [22]).

We conclude with the definition of Chebyshev distance [11].

Keywords: second-countable; intervals; Chebyshev distance

MSC 2010: 54E35; 03B35


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About the article

Received: 2015-12-31

Published Online: 2016-12-08

Published in Print: 2016-06-01

Citation Information: Formalized Mathematics, Volume 24, Issue 2, Pages 121–141, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.1515/forma-2016-0010.

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© 2016 Roland Coghetto, published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. BY-SA 3.0

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