feat: add path component of the identity in a locally path connected topological group, as an open normal subgroup

[j-loreaux]

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From LeanOA

[github-actions]

PR summary 18be37ccef

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Topology.Connected.PathComponentOne (new file)	1213

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Declarations diff

+ IsPathConnected.inv
+ Joined.inv
+ Joined.listProd
+ JoinedIn.inv
+ OpenNormalSubgroup.pathComponentOne
+ Subgroup.Normal.pathComponentOne
+ Subgroup.pathComponentOne
+ Submonoid.pathComponentOne
+ instance [Group G] [IsTopologicalGroup G] [LocPathConnectedSpace G] :
+ inv
- mul_apply

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).