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
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metric space::noun | Spocien Dictionary
| Type | Words |
|---|---|
| Type of | mathematical space, topological space |
| Has types | euclidean space, hilbert space |
Examples of metric space
metric space
Ie electrons in their orbits may well be following space-time metric curvatures.
From the newscientist.com
The FLRW metric starts with the assumption of homogeneity and isotropy of space.
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We can then introduce a metric, making the symmetric group into a metric space.
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Not every finite metric space can be isometrically embedded in a Euclidean space.
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A metric space is now considered a special case of a general topological space.
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Without a metric space, any notion of distance, physical or otherwise is undefined.
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Every separable metric space is homeomorphic to a subset of the Hilbert cube.
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A Polish space with a distinguished complete metric is called a Polish metric space.
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In fact in general, the notion of differentiability is not defined on a metric space.
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