axioms of metric

См. также в других словарях:

• Metric (mathematics) — In mathematics, a metric or distance function is a function which defines a distance between elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set but not all topologies can be generated by a metric …   Wikipedia

• History of the separation axioms — In general topology, the separation axioms have had a convoluted history, with many competing meanings for the same term, and many competing terms for the same concept. Origins Before the current general definition of topological space, there… …   Wikipedia

• Tarski's axioms — Tarski s axioms, due to Alfred Tarski, are an axiom set for the substantial fragment of Euclidean geometry, called elementary, that is formulable in first order logic with identity, and requiring no set theory. Other modern axiomizations of… …   Wikipedia

• Word metric — In group theory, a word metric on a group G is a way to measure distance between any two elements of G . As the name suggests, the word metric is a metric on G , assigning to any two elements g , h of G a distance d(g,h) that measures how… …   Wikipedia

• Wasserstein metric — In mathematics, the Wasserstein (or Vasershtein) metric is a distance function defined between probability distributions on a given metric space M. Intuitively, if each distribution is viewed as a unit amount of dirt piled on M, the metric is the …   Wikipedia

• Glossary of topology — This is a glossary of some terms used in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology. The following definitions are also… …   Wikipedia

• Space (mathematics) — This article is about mathematical structures called spaces. For space as a geometric concept, see Euclidean space. For all other uses, see space (disambiguation). A hierarchy of mathematical spaces: The inner product induces a norm. The norm… …   Wikipedia

• Euclidean geometry — A Greek mathematician performing a geometric construction with a compass, from The School of Athens by Raphael. Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his… …   Wikipedia

• Projective geometry — is a non metrical form of geometry, notable for its principle of duality. Projective geometry grew out of the principles of perspective art established during the Renaissance period, and was first systematically developed by Desargues in the 17th …   Wikipedia

• Construction of the real numbers — In mathematics, there are several ways of defining the real number system as an ordered field. The synthetic approach gives a list of axioms for the real numbers as a complete ordered field. Under the usual axioms of set theory, one can show that …   Wikipedia

• topology — topologic /top euh loj ik/, topological, adj. topologically, adv. topologist, n. /teuh pol euh jee/, n., pl. topologies for 3. Math. 1. the study of those properties of geometric forms that remain invariant under c …   Universalium