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Formalized Mathematics

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Volume 24, Issue 2 (Jun 2016)

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Chebyshev Distance

Roland Coghetto
  • Rue de la Brasserie 5, 7100 La Louvière, Belgium
Published Online: 2016-12-08 | DOI: https://doi.org/10.1515/forma-2016-0010

Summary

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

References

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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, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.1515/forma-2016-0010. Export Citation

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

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