feat(Topology/Connected): connected and path components of products and pi types

[korbonits]

Add connectedComponent_prod/pi and pathComponent_prod/pi: the (path) component of a point in a product is the product of the components of its coordinates. Also add the missing Joined.map, Joined.prod, Joined.pi along the way.

Follow-up to #40092.

[github-actions]

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[github-actions]

PR summary a1e3877848

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ Joined.map
+ Joined.pi
+ Joined.prod
+ connectedComponent_pi
+ connectedComponent_prod
+ pathComponent_pi
+ pathComponent_prod

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

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

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit a1e3877).

• +7 new declarations
• −0 removed declarations

+Joined.map
+Joined.pi
+Joined.prod
+connectedComponent_pi
+connectedComponent_prod
+pathComponent_pi
+pathComponent_prod

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit a1e3877848
Reference commit f34e762642

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/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).

[korbonits]

LLM-generated