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Refactor metric spaces #1450

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@malarbol malarbol commented Jul 9, 2025

Refactoring the metric space module (#1421)

  • remove the notion of Premetric / Premetric-Space:

    as we discussed, the term "premetric" has too many different meanings to be reliably used in this library. What was called a Premetric is now a Rational-Neighborhood-Relation and we only focus on (pseudo)metric spaces.

  • all (pseudo)metric spaces are saturated:

    including saturation in the definition of pseudometric space is coherent with the definition of Richman premetric spaces and makes a lot of things easier (e.g.: the limit map is short, the metric space of Cauchy approximations in a complete metric space is complete, etc.).

  • simplify hierarchy in concepts (define things for for metric spaces first, instead of the splitting premetric>pseudometric>metric):

    although a lot of concepts only depend on the underlying neighborhood relation, they are principally useful for (pseudo)metric spaces. We prioritized definitions on metric spaces, which is where they're the most useful; if we need the corresponding concepts for pseudometric spaces, we can add them later. (e.g. we'll probably want isometry-Pseudometric-Space at some point but I think this PR is already big enough).

@malarbol malarbol marked this pull request as draft July 9, 2025 00:38
@malarbol malarbol self-assigned this Jul 9, 2025
@malarbol malarbol mentioned this pull request Jul 9, 2025
@malarbol malarbol marked this pull request as ready for review July 10, 2025 18:41
@malarbol malarbol mentioned this pull request May 3, 2025
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