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

缝纫

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

狂乱

multiply

Optic-Disk

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

Fulsome

懒洋洋

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.