Examples of 'metric space' in a sentence
Meaning of "metric space"
metric space: In mathematics, a metric space is a set where a distance function (metric) is defined, allowing the measurement of distances between elements
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- Any set on which a metric is defined, giving a distance between any two elements.
How to use "metric space" in a sentence
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metric space
Every metric space is also a topological space.
See also notions of metric space equivalence.
A metric space is a space equipped with a notion of distance.
A set with a metric is called a metric space.
Every discrete metric space is bounded.
Constructions show that every metric space.
Every proper metric space is complete.
Polyhedral space is a certain metric space.
Every metric space is first countable.
A space is metrizable if it is homeomorphic to a metric space.
Every isometry group of a metric space is a subgroup of isometries.
Let be a complete separable metric space.
Every metric space is a closeness space.
Also every subspace of a separable metric space is separable.
Every metric space is paracompact.
See also
Is also а complete separable metric space.
Note that any metric space is completely normal.
This generalises the notion of a complete metric space.
Let be a compact hyperconvex metric space and a continuous mapping.
Let and be two nonempty subsets of a metric space.
A metric space is now considered a special case of a general topological space.
A space is topologically complete if it is homeomorphic to a complete metric space.
A finite metric space is a metric space having a finite number of points.
Menger curvature may also be defined on a general metric space.
The generic name of this metric space is the hyperbolic plane.
Recall that a continuum is a nonempty connected compact metric space.
A metric space is compact if and only if it is complete and totally bounded.
Uniform structure of a metric space.
Metric space completion.
This is because is a metric space.
A metric space is said to be locally compact if every point has a compact neighborhood.
It is assumed that is a metric space.
This topology on a metric space is called the topology induced by the metric d.
Show that closed subspace of a complete metric space is complete.
The metric space formed in this way from a polyhedron is called its development.
Complete metric space.
Real numbers form a topological space and a complete metric space.
Finite metric space.
Prove that the components of a closed subset of a metric space are closed.
Polish metric space.
Every normed space is both a linear topological space and a metric space.
Discrete metric space.
The positive real numbers with distance function is a complete metric space.
Is also a metric space.
A metric space is a collection of objects together with a notion of distance between these objects.
Difference between complete metric space and completely metrizable space.
Therefore only in special cases this distance makes a collection of sets a metric space.
Proper metric space.
All it needs is the distance function that satisfies the properties of the metric space.
Geodesic metric space.
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