[Merged by Bors] - feat(Analysis): PathConnectedSpace ℂˣ

[erdOne]

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[github-actions]

PR summary 1f85fdff73

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

+ instance : PathConnectedSpace ℂˣ

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).

[j-loreaux]

bors d+

[j-loreaux]

Please add a comment explaining that this could be proved faster using other means (e.g., via the exponential map, or via facts about real vector spaces of dimension exceeding one), but that this approach was adopted to minimize imports.

[mathlib-bors]

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

[Komyyy]

I think this proof can be golfed using isPathConnected_compl_singleton_of_one_lt_rank.

[erdOne]

Yes but it requires a lot more import. But this is a valid point and is also what Jireh has suggested.

[Komyyy]

Sorry, I didn't read @j-loreaux 's comments, please forget.

[erdOne]

bors merge

[mathlib-bors]

Pull request successfully merged into master.

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