Titlebook: Encyclopedia of Distances; Michel Marie Deza,Elena Deza Book 2016Latest edition Springer-Verlag Berlin Heidelberg 2016 distance.metric spa

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Production Development over Time,Here we consider the most important metrics on the classical number systems: the semiring . of natural numbers, the ring . of integers, and the fields ., ., . of rational, real, complex numbers, respectively. We consider also the algebra . of quaternions.

衣服

狂亂

multiply

Optic-Disk

General DefinitionsA .(.,?.) is a set . (.) equipped with a . ..

Fulsome

懶洋洋

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.

cunning

AXIOM

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.

fixed-joint

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.