[Merged by Bors] - feat(Topology/Algebra/Group/Basic): group is totally disconnected iff connectedComponent 1 = {1}

[tb65536]

This PR proves that a group G is totally disconnected if and only if connectedComponent 1 = {1}.

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[github-actions]

PR summary 4827413258

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

+ smul_connectedComponent
+ totallyDisconnectedSpace_iff_connectedComponent_one

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 scripts/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]

thanks!

bors merge

[bryangingechen]

There is a merge conflict.
bors r-
bors d+

[mathlib-bors]

✌️ tb65536 can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[mathlib-bors]

Canceled.

[tb65536]

bors r+

[mathlib-bors]

Build failed:

• ci (staging) / Post-CI job

[sgouezel]

bors r+

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• ci (staging) / Post-Build Step
• ci (staging) / Build
• ci (staging) / Post-CI job
• ci (staging) / Lint style