<abstract xmlns="http://www.w3.org/1999/xhtml">In <xref ref-type="bibr" rid="j_forma-2016-0010_ref_021_w2aab2b8b7b1b7b1ab1ac21Aa">[21]</xref>, Marco Riccardi formalized that ℝN-basis <italic>n</italic> is a basis (in the algebraic sense defined in <xref ref-type="bibr" rid="j_forma-2016-0010_ref_026_w2aab2b8b7b1b7b1ab1ac26Aa">[26]</xref>) of <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_forma-2016-0010_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mi>ℰ</mi><mi>T</mi><mi>n</mi></msubsup></mrow></math><tex-math>${\cal E}_T^n $</tex-math></alternatives></inline-formula> and in <xref ref-type="bibr" rid="j_forma-2016-0010_ref_020_w2aab2b8b7b1b7b1ab1ac20Aa">[20]</xref> he has formalized that <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_forma-2016-0010_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mi>ℰ</mi><mi>T</mi><mi>n</mi></msubsup></mrow></math><tex-math>${\cal E}_T^n $</tex-math></alternatives></inline-formula> is second-countable, we build (in the topological sense defined in <xref ref-type="bibr" rid="j_forma-2016-0010_ref_023_w2aab2b8b7b1b7b1ab1ac23Aa">[23]</xref>) a denumerable base of <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_forma-2016-0010_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mi>ℰ</mi><mi>T</mi><mi>n</mi></msubsup></mrow></math><tex-math>${\cal E}_T^n $</tex-math></alternatives></inline-formula>.Then we introduce the <italic>n</italic>-dimensional intervals (interval in <italic>n</italic>-dimensional Euclidean space, <italic>pavé (borné) de</italic> ℝ<italic>n</italic><xref ref-type="bibr" rid="j_forma-2016-0010_ref_016_w2aab2b8b7b1b7b1ab1ac16Aa">[16]</xref>, <italic>semi-intervalle (borné) de</italic> ℝ<italic>n</italic><xref ref-type="bibr" rid="j_forma-2016-0010_ref_022_w2aab2b8b7b1b7b1ab1ac22Aa">[22]</xref>).We conclude with the definition of Chebyshev distance <xref ref-type="bibr" rid="j_forma-2016-0010_ref_011_w2aab2b8b7b1b7b1ab1ac11Aa">[11]</xref>.</abstract>

In [21], Marco Riccardi formalized that ℝN-basis n is a basis (in the algebraic sense defined in [26]) of ℰTn${\cal E}_T^n $ and in [20] he has formalized that ℰTn${\cal E}_T^n $ is second-countable, we build (in the topological sense defined in [23]) a denumerable base of ℰTn${\cal E}_T^n $.Then we introduce the n-dimensional intervals (interval in n-dimensional Euclidean space, pavé (borné) de ℝn[16], semi-intervalle (borné) de ℝn[22]).We conclude with the definition of Chebyshev distance [11].

Chebyshev Distance

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Formalized Mathematics

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{"article-title":"Chebyshev Distance"}

In [21], Marco Riccardi formalized that ℝN-basis n is a basis (in the algebraic sense defined in [26]) of ℰTn${\cal E}_T^n $ and in [20] he has formalized that...

Chebyshev Distance

Published Online: Dec 08, 2016

Page range: 121 - 141

Received: Dec 31, 2015

DOI: https://doi.org/10.1515/forma-2016-0010

Keywords
second-countable, intervals, Chebyshev distance

© 2016 Roland Coghetto, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Chebyshev Distance

Published Online: Dec 08, 2016

Page range: 121 - 141

Received: Dec 31, 2015

DOI: https://doi.org/10.1515/forma-2016-0010

Keywordssecond-countable, intervals, Chebyshev distance

© 2016 Roland Coghetto, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Keywords
second-countable, intervals, Chebyshev distance