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Cauchy precompletions of pseudometric spaces #1640
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…agda.md Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
…agda.md Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
…es.lagda.md Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
…es.lagda.md Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
…es.lagda.md Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
…es.lagda.md Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
…es.lagda.md Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
…es.lagda.md Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
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This is my follow up on #1458. As I commented before, this Cauchy precompletion is the closest to a Cauchy completion I could get. |
| (f : isometry-Pseudometric-Space A B) | ||
| where | ||
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| map-isometry-cauchy-approximation-Pseudometric-Space : |
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| map-isometry-cauchy-approximation-Pseudometric-Space : | |
| map-cauchy-approximation-isometry-Pseudometric-Space : |
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Re-drafting this PR to split in and formalize a few results about metric extensions before talking about Cauchy precompletions. And maybe rework a bit the construction of |
This PR introduces the following concepts:
The Cauchy precompletion of a pseudometric space is Cauchy dense and any metric extension into a complete metric
space factors through its Cauchy precompletion.