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Built on top of #1726.

This PR introduces the concept of Cauchy metric extensions of a pseudometric spaces: metric extensions f : P → M such that there exists some g : C P → M satisfying

  g ∘ κ ~ f

where C P is the cauchy pseudocompletion of P and κ : P → C P the natural isometry of cauchy pseudocompletions.

Any such g is unique and Cauchy metric extensions are equivalent to metric extensions of Cauchy pseudocompletions.

malarbol and others added 30 commits November 22, 2025 18:28
…dometric-spaces.lagda.md

Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
…dometric-spaces.lagda.md

Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
…dometric-spaces.lagda.md

Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
…dometric-spaces.lagda.md

Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
…dometric-spaces.lagda.md

Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
@malarbol malarbol marked this pull request as draft December 1, 2025 19:09
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