[Merged by Bors] - feat: topology on ring of finite adeles.

[kbuzzard]

Use SubmodulesRingBasis to put a topology on the finite adeles.

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Remark: when this work was WIP and depended on other PRs it was #13703 (with no reviewer comments). Now all the PRs it depended on are merged, I merged master, it picked up a conflict, and I somehow messed up resolving it, with github reporting hundreds of changed files (edit: the problem was that I merged master after a dependent PR was squash-merged, and I had my git config set to "rebase when pulling by default"). So I've opened this, a new PR with the same material.

[github-actions]

PR summary ae4a748d58

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

+ adicCompletion.mul_nonZeroDivisor_mem_adicCompletionIntegers
+ coe_mem_adicCompletionIntegers
+ exists_finiteIntegralAdele_iff
+ instance : Algebra R (FiniteAdeleRing R K)
+ instance : CoeFun (FiniteAdeleRing R K)
+ instance : IsScalarTower R K (FiniteAdeleRing R K)
+ instance : TopologicalSpace (FiniteAdeleRing R K)
+ intValuationDef_zero
+ mul_nonZeroDivisor_mem_finiteIntegralAdeles
+ not_mem_adicCompletionIntegers
+ submodulesRingBasis
+ valuation_eq_intValuationDef
+ valuedAdicCompletion_eq_valuation
+ valuedAdicCompletion_eq_valuation'

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>

[riccardobrasca]

Thanks!

bors d+

[mathlib-bors]

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[kbuzzard]

bors r+

[mathlib-bors]

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[kbuzzard]

bors r+

[mathlib-bors]

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