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[Merged by Bors] - feat(topology/metric_space): a countably generated uniformity is metrizable #14052

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[Merged by Bors] - feat(topology/metric_space): a countably generated uniformity is metrizable #14052

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@urkud urkud commented May 9, 2022 •
edited by github-actions bot

@urkud urkud added the WIP Work in progress label May 9, 2022
@mathlib-dependent-issues-bot mathlib-dependent-issues-bot added blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. and removed blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. labels May 9, 2022
@mathlib-dependent-issues-bot mathlib-dependent-issues-bot removed the blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. label May 22, 2022
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@urkud urkud added awaiting-review The author would like community review of the PR awaiting-CI The author would like to see what CI has to say before doing more work. and removed WIP Work in progress labels Jun 4, 2022
@github-actions github-actions bot removed the awaiting-CI The author would like to see what CI has to say before doing more work. label Jun 4, 2022
sgouezel
sgouezel reviewed Jun 24, 2022
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src/topology/metric_space/metrizable_uniformity.lean
In this file we prove that a uniform space with countably generated uniformity filter is
pseudometrizable: there exists a `pseudo_metric_space` structure that generates the same uniformity.
The proof follows [Sergey Melikhov, Metrizable uniform spaces][melikhov2011].
-/
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Can you present the API here?

@sgouezel sgouezel added awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-review The author would like community review of the PR labels Jun 24, 2022
fpvandoorn
fpvandoorn reviewed Jun 24, 2022
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LGTM otherwise.

Thanks!

bors d+

src/data/nat/lattice.lean
Comment on lines +114 to +115
lemma Sup_mem {s : set ℕ} (h₁ : s.nonempty) (h₂ : bdd_above s) : Sup s ∈ s :=
let ⟨k, hk⟩ := h₂ in h₁.cSup_mem ((finite_le_nat k).subset hk)
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For int this is called cSup_mem. Also, can this be generalized to a succ_order?

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OTOH, we have nat.Inf_add below. I'll generalize in a follow-up PR.

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bors bot commented Jun 24, 2022

✌️ urkud can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@leanprover-community-bot-assistant leanprover-community-bot-assistant added the delegated The PR author may merge after reviewing final suggestions. label Jun 24, 2022
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urkud commented Jun 24, 2022

bors merge

@github-actions github-actions bot added ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) and removed awaiting-author A reviewer has asked the author a question or requested changes labels Jun 24, 2022
bors bot pushed a commit that referenced this pull request Jun 24, 2022
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feat(topology/metric_space): a countably generated uniformity is metr…
40fa2d8 
…izable (#14052)
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Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat(topology/metric_space): a countably generated uniformity is metrizable [Merged by Bors] - feat(topology/metric_space): a countably generated uniformity is metrizable Jun 24, 2022
@bors bors bot closed this Jun 24, 2022
@bors bors bot deleted the YK-metrizable branch June 24, 2022 21:27
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