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- Coarse_structure abstract ""Coarse space" redirects here. For the use of "coarse space" in numerical analysis, see coarse problem.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.".
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- Coarse_structure wikiPageWikiLink Degrees_of_freedom_(statistics).
- Coarse_structure wikiPageWikiLink Diagonal.
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- Coarse_structure wikiPageWikiLink Integer_lattice.
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- Coarse_structure wikiPageWikiLink Neighbourhood_(mathematics).
- Coarse_structure wikiPageWikiLink Notices_of_the_American_Mathematical_Society.
- Coarse_structure wikiPageWikiLink Open_set.
- Coarse_structure wikiPageWikiLink PDF.
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- Coarse_structure wikiPageWikiLink Projection_(relational_algebra).
- Coarse_structure wikiPageWikiLink Quasi-isometry.
- Coarse_structure wikiPageWikiLink Relatively_compact_subspace.
- Coarse_structure wikiPageWikiLink Set_(mathematics).
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- Coarse_structure wikiPageWikiLink Subsets.
- Coarse_structure wikiPageWikiLink Topological_space.
- Coarse_structure wikiPageWikiLink Topology.
- Coarse_structure wikiPageWikiLink Uniform_metric.
- Coarse_structure wikiPageWikiLink Uniform_norm.
- Coarse_structure wikiPageWikiLink Uniform_space.
- Coarse_structure wikiPageWikiLink Union_(set_theory).
- Coarse_structure wikiPageWikiLinkText "Coarse Structure".
- Coarse_structure wikiPageWikiLinkText "Coarse structure".
- Coarse_structure wikiPageWikiLinkText "coarse geometry".
- Coarse_structure wikiPageWikiLinkText "coarse structure".
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- Coarse_structure wikiPageUsesTemplate Template:Cite_journal.
- Coarse_structure subject Category:Metric_geometry.
- Coarse_structure subject Category:Topology.
- Coarse_structure type Field.
- Coarse_structure comment ""Coarse space" redirects here.".
- Coarse_structure label "Coarse structure".
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- Coarse_structure sameAs Q4502433.
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- Coarse_structure wasDerivedFrom Coarse_structure?oldid=635059503.
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