metric space


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Related to metric space: Complete metric space
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Noun1.metric space - 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
mathematical space, topological space - (mathematics) any set of points that satisfy a set of postulates of some kind; "assume that the topological space is finite dimensional"
Euclidean space - a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional
Hilbert space - a metric space that is linear and complete and (usually) infinite-dimensional
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References in periodicals archive ?
It is easy to show that (X, d) is an asymmetric metric space. Consider T : X [right arrow] X by Tx = 1/2x.
Abstract: In a previous paper of ours we studied a class of nonlinear self-mappings of a complete metric space endowed with a natural metric.
Recently, Ali and Smarandache studied neutrosophic triplet ring and neutrosophic triplet field [17]; Sahin and Kargin obtained neutrosophic triplet normed space [18]; Sahin and Kargin introduced neutrosophic triplet inner product space [19]; Smarandache, Sahin and Kargin studied neutrosophic Triplet G- Module [20]; Bal, Shalla and Olgun obtained neutrosophic triplet cosets and quotient groups [21]; Sahin, Kargin and Coban introduced fixed point theorem for neutrosophic triplet partial metric space [22]; Sahin and Kargin neutrosophic triplet v -generalized metric space [23]; Celik, Shalla and Olgun studied fundamental homomorphism theorems for neutrosophic extended triplet groups [24].
The topics include Kyiv from the fall of 1943 through 1946: the rebirth of mathematics, two consequences of extension of local maps of Banach spaces: applications and examples, Hasse-Schmidt derivations and the Cayley-Hamilton theorem for exterior algebras, some binomial formulae for non-commuting operators, and the complete metric space of Riemann integrable functions and differential calculus in it.
We note that a metric space is evidently a b-metric space for s = 1.
Let X be a complete metric space. Let [p.sub.1], ..., [p.sub.N] [member of] (0,1) such that [[summation].sup.N.sub.i=1] [p.sub.i] = 1.
Let (X, d) be a metric space. The set of all nonempty closed and bounded subsets of X is denoted by CB(X).
Also, it characterizes the completeness of the metric space as showed by Kirk in [9].
Then d is called a generalized metric on X and (X, d) is called a generalized metric space.
The generalization of a metric space is based on reducing or modifying the metric axioms; for example, we cite quasi-metrics, partial metrics, m-metrics, Sp metrics, rectangular metrics, k-metrics.
For s = 1 and g = [I.sub.x] the definition reduces to the definition of an [alpha]-admissible mapping in a metric space [6].
Let (X, d) be a metric space and T : X [right arrow] X be a self-mapping.