Metric quotients of pseudometric spaces #1622
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…agda.md Co-authored-by: Fredrik Bakke <[email protected]>
…agda.md Co-authored-by: Fredrik Bakke <[email protected]>
…es.lagda.md Co-authored-by: Fredrik Bakke <[email protected]>
…es.lagda.md Co-authored-by: Fredrik Bakke <[email protected]>
…es.lagda.md Co-authored-by: Fredrik Bakke <[email protected]>
…es.lagda.md Co-authored-by: Fredrik Bakke <[email protected]>
…es.lagda.md Co-authored-by: Fredrik Bakke <[email protected]>
…es.lagda.md Co-authored-by: Fredrik Bakke <[email protected]>
src/metric-spaces/cauchy-pseudocompletion-of-pseudometric-spaces.lagda.md
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…es.lagda.md Co-authored-by: Fredrik Bakke <[email protected]>
…a.md Co-authored-by: Fredrik Bakke <[email protected]>
src/metric-spaces/metric-quotients-of-pseudometric-spaces.lagda.md
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…a.md Co-authored-by: Fredrik Bakke <[email protected]>
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…a.md Co-authored-by: Fredrik Bakke <[email protected]>
…a.md Co-authored-by: Fredrik Bakke <[email protected]>
src/metric-spaces/cauchy-approximations-metric-quotients-of-pseudometric-spaces.lagda.md
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fredrik-bakke
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Nov 6, 2025
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This contribution is really well done, thank you for contributing it @malarbol. Sorry it took so long to review it
…eudometric-spaces.lagda.md
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Is the co-authorship tag on this PR correct? As far as I can see this work has been pretty independent? |
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This PR introduces the notion of metric quotient of a pseudometric spaces: the metric space whose objects are quotient classes under the similarity relation in the pseudometric spaces and rational neighborhood relations given by neighborhoods of class-elements.
This is a metric space isometric to the original pseudometric space. In case of metric spaces, this isometry is an isometric equivalence. Any short map (resp. isometry) from a pseudometric space to a metric space factors as a short map (resp. isometry) through the metric quotient.
The module
cauchy-approximations-metric-quotients-of-pseudometric-spacesintroduces a few results regarding Cauchy approximations in pseudometric spaces and Cauchy approximations in their metric quotients.Co-authored-by: Louis Wasserman [email protected]