feat(Topology/ContinuousMap): domMulAct action on C(X, Y)

[EzequielS2]

Summary

• Define the action of Mᵈᵐᵃ on C(α, β) when M acts continuously on α.
• Add SMul, MulAction, SMulCommClass, and ContinuousSMul instances.
• Closes Extend basic API about DomMulAct #5379.

Test plan

• lake build Mathlib.Topology.ContinuousMap.DomAct
• lake exe runLinter Mathlib.Topology.ContinuousMap.DomAct

[github-actions]

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[github-actions]

✅ PR Title Formatted Correctly

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[github-actions]

PR summary 2bf435cdd4

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Topology.ContinuousMap.DomAct (new file)	1276

---

Declarations diff (regex)

+ coe_smul_continuousMap
+ instContinuousSMulContinuousMap
+ instMulActionContinuousMap
+ instSMulCommClass_dom
+ instSMulCommClass_left
+ instSMulCommClass_right
+ instSMulContinuousMap
+ mk_smul_continuousMap_apply
+ smul_continuousMap_apply

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 2bf435c).

• +9 new declarations
• −0 removed declarations

+DomMulAct.coe_smul_continuousMap
+DomMulAct.instContinuousSMulContinuousMap
+DomMulAct.instMulActionContinuousMap
+DomMulAct.instSMulCommClass_dom
+DomMulAct.instSMulCommClass_left
+DomMulAct.instSMulCommClass_right
+DomMulAct.instSMulContinuousMap
+DomMulAct.mk_smul_continuousMap_apply
+DomMulAct.smul_continuousMap_apply

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 2bf435cdd4
Reference commit 308db4b777

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).