Titlebook: Encyclopedia of Distances; Michel Marie Deza,Elena Deza Book 20143rd edition Springer-Verlag Berlin Heidelberg 2014 distance.metric space.

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General DefinitionsIn this core Chapter, the main metrics and metric-related notions are given.

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Distances in Geometry. arose as the field of knowledge dealing with spatial relationships. It was one of the two fields of pre-modern Mathematics, the other being the study of numbers.

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Distances in AlgebraA . (., ⋅ , .) is a set . of elements with a binary operation ⋅ , called the ., that together satisfy the four fundamental properties of . (. ⋅ . ∈ . for any ., . ∈ .), . (. ⋅ (. ⋅ .) = (. ⋅ .) ⋅ . for any ., ., . ∈ .), the . (. for any . ∈ .), and the . (for any . ∈ ., there exists an element .. ∈ . such that .

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Titlebook: Encyclopedia of Distances; Michel Marie Deza,Elena Deza Book 20143rd edition Springer-Verlag Berlin Heidelberg 2014 distance.metric space.

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