Search results
Results from the WOW.Com Content Network
Functions to a metric space. If X is any set and M is a metric space, then the set of all bounded functions: (i.e. those functions whose image is a bounded subset of ) can be turned into a metric space by defining the distance between two bounded functions f and g to be (,) = ((), ()).
The space M' is determined up to isometry by this property (among all complete metric spaces isometrically containing M), and is called the completion of M. The completion of M can be constructed as a set of equivalence classes of Cauchy sequences in M.
The space Aim(X) is injective (hyperconvex in the sense of Aronszajn-Panitchpakdi) – given a metric space M, which contains Aim(X) as a metric subspace, there is a canonical (and explicit) metric retraction of M onto Aim(X) (Holsztyński 1966).
In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. The metric captures all the geometric and causal structure of spacetime , being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past.
In mathematics, a contraction mapping, or contraction or contractor, on a metric space (M, d) is a function f from M to itself, with the property that there is some real number < such that for all x and y in M, ((), ()) (,).
Namely, let X and Y be two compact figures in a metric space M (usually a Euclidean space); then D H (X,Y) is the infimum of d H (I(X),Y) among all isometries I of the metric space M to itself. This distance measures how far the shapes X and Y are from being isometric.
Let (M, d) be a metric space, let K be a subset of M, and let r be a positive real number.Let B r (x) denote the ball of radius r centered at x.A subset C of M is an r-external covering of K if:
Pages in category "Metric spaces" The following 13 pages are in this category, out of 13 total. ... M. Metric lattice; Metric projection; Metrizable space;