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refactor(LocallyConvex,Topology): split WeakDual/WeakSpace and rename WeakBilin#37027

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refactor(LocallyConvex,Topology): split WeakDual/WeakSpace and rename WeakBilin#37027
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@mike1729 mike1729 commented Mar 23, 2026

Reorganize the weak topology files for cleaner dependencies:

  1. Rename Analysis.LocallyConvex.WeakDualAnalysis.LocallyConvex.WeakBilin:
    This file contains only general WeakBilin infrastructure (LinearMap.toSeminormFamily,
    weakBilin_withSeminorms, WeakBilin.locallyConvexSpace, etc.) with no reference to
    WeakDual. The name now reflects the content.

  2. Split Topology.Algebra.Module.WeakDual into WeakDual and WeakSpace:
    The WeakSpace type, its instances, and toWeakSpace/toWeakSpaceCLM move to a new
    Topology.Algebra.Module.WeakSpace. This allows downstream files about weak spaces
    to avoid depending on WeakDual.

  3. Add WeakSpace.seminormFamily and WeakSpace.withSeminorms to
    Analysis.LocallyConvex.WeakSpace: The weak topology on WeakSpace 𝕜 E is generated
    by the seminorm family fun f x ↦ ‖f x‖ indexed by StrongDual 𝕜 E, via the general
    LinearMap.weakBilin_withSeminorms applied to the flipped topDualPairing.

Moves:

  • Mathlib.Analysis.LocallyConvex.WeakDual -> Mathlib.Analysis.LocallyConvex.WeakBilin
  • WeakSpace -> Mathlib.Topology.Algebra.Module.WeakSpace
  • toWeakSpace -> Mathlib.Topology.Algebra.Module.WeakSpace
  • toWeakSpaceCLM -> Mathlib.Topology.Algebra.Module.WeakSpace

CC @j-loreaux


@github-actions github-actions bot added the new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! label Mar 23, 2026
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github-actions bot commented Mar 23, 2026

PR summary 6cad1b0fcc

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.Analysis.LocallyConvex.WeakDual -1805
Mathlib.Analysis.LocallyConvex.WeakSpace Mathlib.Analysis.Normed.Module.DoubleDual 1
Mathlib.Topology.Algebra.Module.WeakSpace (new file) 1210
Mathlib.Analysis.LocallyConvex.WeakBilin 1805

Declarations diff

+ seminormFamily
+ seminormFamily_apply
+ withSeminorms

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.


Increase in tech debt: (relative, absolute) = (3.00, 0.00)
Current number Change Type
7426 3 backward.isDefEq

Current commit 9c598f700d
Reference commit 6cad1b0fcc

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).

note: file Mathlib/Analysis/LocallyConvex/WeakDual.lean` was renamed to `Mathlib/Analysis/LocallyConvex/WeakBilin.lean without a module deprecation
Please create a follow-up pull request adding one. Thanks!

@github-actions github-actions bot added the file-removed A Lean module was (re)moved without a `deprecated_module` annotation label Mar 23, 2026
@mathlib-merge-conflicts mathlib-merge-conflicts bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Mar 25, 2026
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This pull request has conflicts, please merge master and resolve them.

@github-actions github-actions bot removed the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Mar 25, 2026
# Conflicts:
#	Mathlib/Analysis/LocallyConvex/WeakSpace.lean
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I'm going to make this wait for #37314 as they will conflict.

@j-loreaux j-loreaux added the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Mar 31, 2026
@mathlib-dependent-issues mathlib-dependent-issues bot removed the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Apr 3, 2026
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