metric space

Any space whose elements are points, and between any two of which a nonnegative real number can be defined as the distance between the points; an example is Euclidean space
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Metric space — In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined. The metric space which most closely corresponds to our intuitive understanding of space is the 3 dimensional Euclidean… … Wikipedia
metric space — Math. a space with a metric defined on it. [1925 30] * * * In mathematics, a set of objects equipped with a concept of distance. The objects can be thought of as points in space, with the distance between points given by a distance formula, such… … Universalium
metric space — metrinė erdvė statusas T sritis fizika atitikmenys: angl. metric space vok. metrischer Raum, m rus. метрическое пространство, n pranc. espace métrique, m … Fizikos terminų žodynas
metric space — noun a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality • Hypernyms: ↑mathematical space, ↑topological space • Hyponyms: ↑Euclidean… … Useful english dictionary
metric space — noun Date: 1927 a mathematical set for which a metric is defined for any pair of elements … New Collegiate Dictionary
Metric space aimed at its subspace — In mathematics, a metric space aimed at its subspace is a categorical construction that has a direct geometric meaning. It is also a useful step toward the construction of the metric envelope, or tight span, which are basic (injective) objects of … Wikipedia
Complete metric space — Cauchy completion redirects here. For the use in category theory, see Karoubi envelope. In mathematical analysis, a metric space M is called complete (or Cauchy) if every Cauchy sequence of points in M has a limit that is also in M or,… … Wikipedia
Convex metric space — An illustration of a convex metric space. In mathematics, convex metric spaces are, intuitively, metric spaces with the property any segment joining two points in that space has other points in it besides the endpoints. Formally, consider a… … Wikipedia
Injective metric space — In metric geometry, an injective metric space, or equivalently a hyperconvex metric space, is a metric space with certain properties generalizing those of the real line and of L∞ distances in higher dimensional vector spaces. These properties can … Wikipedia
Probabilistic metric space — A probabilistic metric space is a generalization of metric spaces where the distance is no longer defined on positive real numbers, but on distribution functions. Let D + be the set of all probability distribution functions F such that F (0) = 0… … Wikipedia