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 ?
Definition 4.12: Let (([N.sub.1]), [d.sub.1]) and (([N.sub.2], *), [d.sub.2]) be NT metric spaces, [mathematical expression not reproducible] and [mathematical expression not reproducible] be NT metric topologies.
They give a unified definition of curvature that applies to a wide class of geometric structures whose geodesics arise from optimal control problems, including Riemannian, sub-Riemannian, Finsler, and sub-Finsler spaces, but pay special attention to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Their construction of curvature is direct and naive, they say, similar to the original approach of Riemann.
[2] Bojor, F, Fixed point theorems for Reich type contraction on metric spaces with a graph, Nonlinear Anal.
In 2012, Abdeljawad et al.'s paper [10] contains a study of M-K type coupled fixed point on ordered partial metric spaces and Chen et al.
An analogue version of Theorem 10 in the setting of the preordered metric spaces may be stated as follows.
Branciari [1] introduced the notion of generalized metric spaces and obtained a generalization of the Banach contraction principle, whereafter many authors proved various fixed point results in such spaces, for example, [2-8] and references therein.
In [15], the notion of a rectangular metric space was extended to rectangular partial metric spaces as follows.
Recently some authors have introduced some generalizations of metric spaces in several ways and have studied fixed point problems in these spaces, as well as their applications.
On the other hand, Bakhtin [6] and Czerwik [7] introduced the concept of b-metric spaces (a generalization of metric spaces) and proved the Banach contraction principle.
Chairman Department of Mathematics Government College University Lahore Dr Mujahid Abbas shared his views on 'Multivalued Mapping in Fuzzy Metric Spaces'.
are equivalent for all metric spaces (X, [rho]), ([A.sub.k]) [subset] CL(X) and A [member of] CL(X).