Metric quotients of pseudometric spaces #1622
Merged
Conversation
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
…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]>
Collaborator
Author
src/metric-spaces/cauchy-pseudocompletion-of-pseudometric-spaces.lagda.md
Outdated
Show resolved
Hide resolved
src/metric-spaces/metric-quotients-of-pseudometric-spaces.lagda.md
Outdated
Show resolved
Hide resolved
src/metric-spaces/metric-quotients-of-pseudometric-spaces.lagda.md
Outdated
Show resolved
Hide resolved
…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
Outdated
Show resolved
Hide resolved
…a.md Co-authored-by: Fredrik Bakke <[email protected]>
src/metric-spaces/metric-quotients-of-pseudometric-spaces.lagda.md
Outdated
Show resolved
Hide resolved
…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
Outdated
Show resolved
Hide resolved
fredrik-bakke
approved these changes
Nov 6, 2025
Collaborator
fredrik-bakke
left a comment
fredrik-bakke
left a comment
There was a problem hiding this comment.
This contribution is really well done, thank you for contributing it @malarbol. Sorry it took so long to review it
…eudometric-spaces.lagda.md
Collaborator
|
Is the co-authorship tag on this PR correct? As far as I can see this work has been pretty independent? |
Collaborator
Author
Yes it is correct. I learned this construction from @lowasser in #1458 (comment) |
Collaborator
Author
|
Thanks a lot for your review and your patience. |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
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]