Coarse Structure

(Metric Geometry)

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sciences
Metric Geometry
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What is Coarse structure?

In the mathematical fields of geometry and topology, a coarse structure on a set X is a collection of subsets of the cartesian product X × X with certain properties which allow the large-scale structure of metric spaces and topological spaces to be defined. The concern of traditional geometry and topology is with the small-scale structure of the space: properties such as the continuity of a function depend on whether the inverse images of small open sets, or neighborhoods, are themselves open. Large-scale properties of a space—such as boundedness, or the degrees of freedom of the space—do not depend on such features. Coarse geometry and coarse topology provide tools for measuring the large-scale properties of a space, and just as a metric or a topology contains information on the small-scale structure of a space, a coarse structure contains information on its large-scale properties. Properly, a coarse structure is not the large-scale analog of a topological structure, but of a uniform structure.

Technology Types

metric geometrytopology

Synonyms

Coarse geometryCoarse space

Translations

هيكل إجمالي (ar)粗空間 (ja)

Tech Info


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