[Merged by Bors] - feat: a finite space is Baire.

[CoolRmal]

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[github-actions]

PR summary d68c4dc09f

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ Set.Finite.dense_sInter
+ baire_of_finite

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[j-loreaux]

Why do you want this? It seems an odd thing to care about whether a finite space is Baire.

Nevertheless, the first lemma is nice.

[CoolRmal]

@j-loreaux It is just a random fact I saw on wikipedia and I found it easy to formalize. It is totally fine if you don't think it worth to be put into Mathlib.

[CoolRmal]

-awaiting-author

[j-loreaux]

Make it a theorem instead of an instance and we'll call it good.

[CoolRmal]

@j-loreaux It is indeed a theorem right now.

[j-loreaux]

Oh, oops! Sorry.

[j-loreaux]

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded!

And happy new year! 🎉

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