feat: if E is finite dimensional, E →L[𝕜] F has the product topology

[ADedecker]

---

• depends on: [Merged by Bors] - feat: ContinuousLinearMap.continuous_of_continuous_uncurry #36776
• depends on: [Merged by Bors] - feat: MonoidHom.isUniformEmbedding_of_isEmbedding #36870
• depends on: feat: ContinuousLinearMap.pi as a continuous linear equivalence #37435
• depends on: feat: UniformConvergenceCLM version of ContinuousLinearEquiv.arrowCongr #37439
• depends on: feat: notation for UniformConvergenceCLM #37614

[github-actions]

PR summary 8f1377de1f

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Topology.Algebra.Module.FiniteDimensionStrongTopology (new file)	1961

---

Declarations diff

+ ContinuousLinearMap.flipOfFiniteDimensional
+ ContinuousLinearMap.flipOfFiniteDimensional_apply
+ ContinuousLinearMap.flipOfFiniteDimensional_symm_apply
+ ContinuousLinearMap.isEmbedding_coeFn_of_finiteDimensional
+ ContinuousLinearMap.isUniformEmbedding_coeFn_of_finiteDimensional
+ Module.Basis.constrCLE
+ Module.Basis.continuous_constrL
+ UniformConvergenceCLM.piEquivL
+ arrowCongrEquivₛₗ
+ constrCLE
+ continuous_constrL
+ flipOfBasis
+ flipOfBasis_apply
+ flipOfBasis_symm_apply
+ flipOfFiniteDimensional
+ flipOfFiniteDimensional_apply
+ flipOfFiniteDimensional_symm_apply
+ isEmbedding_coeFn_of_finiteDimensional
+ isUniformEmbedding_coeFn_of_finiteDimensional
+ piEquivL
+ uniformConvergenceCLMCongr
+ uniformConvergenceCLMCongrSL

You can run this locally as follows

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

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

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./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).

[eric-wieser]

Suggested change

	protected noncomputable def Module.Basis.constrLCLE [Finite ι] (b : Basis ι 𝕜 E) :
	protected noncomputable def Module.Basis.constrCLE [Finite ι] (b : Basis ι 𝕜 E) :

[eric-wieser]

Oh nevermind. I think a docstring would have helped my confusion.

[ADedecker]

I agree that constrCLE reads better. It is a bit less precise, but maybe that's okay? As in, because there's topology around, it's clear from context that we are talking about continuous linear maps?

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.

[mathlib-dependent-issues]

This PR/issue depends on:

• [Merged by Bors] - feat: ContinuousLinearMap.continuous_of_continuous_uncurry #36776
• [Merged by Bors] - feat: MonoidHom.isUniformEmbedding_of_isEmbedding #36870
• feat: ContinuousLinearMap.pi as a continuous linear equivalence #37435
• feat: UniformConvergenceCLM version of ContinuousLinearEquiv.arrowCongr #37439
• feat: notation for UniformConvergenceCLM #37614
  By Dependent Issues (🤖). Happy coding!

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.