Titlebook: Encyclopedia of Distances; Michel Marie Deza,Elena Deza Book 20132nd edition Springer-Verlag Berlin Heidelberg 2013 distance.metric space.

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Generalizations of Metric SpacesSome immediate generalizations of the notion of metric, for example, ., ., ., were defined in Chap. .. Here we give some generalizations in the direction of Topology, Probability, Algebra, etc.

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载货清单

Metrics on Normed StructuresIn this chapter we consider a special class of metrics defined on some ., as the norm of the difference between two given elements. This structure can be a group (with a .), a vector space (with a . or, simply, a .), a vector lattice (with a .), a field (with a .), etc.

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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.

Aromatic

Distances on Surfaces and KnotsA . is a real two-dimensional . . ., i.e., a ., each point of which has a neighborhood which is homeomorphic to a plane ., or a closed half-plane (cf. Chap. .).

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WITH

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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天真

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