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feat(Analysis/Normed/Module): add bornology and T2 instances for WeakSpace#37161

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mike1729:bornology-weakspace
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feat(Analysis/Normed/Module): add bornology and T2 instances for WeakSpace#37161
mike1729 wants to merge 10 commits intoleanprover-community:masterfrom
mike1729:bornology-weakspace

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Register the norm bornology on WeakSpace 𝕜 E and prove that it coincides with the von Neumann bornology of the weak topology.

New declarations

  • WeakSpace.instBornology: norm bornology inherited from E.
  • WeakSpace.instT2Space: Hausdorff via Hahn–Banach separation.
  • WeakSpace.norm_topology_le_weakSpace_topology: the weak topology is coarser than the norm topology.
  • WeakSpace.isBounded_iff_isVonNBounded: norm-boundedness equals weak von Neumann boundedness (no [CompleteSpace E] needed).

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@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 25, 2026
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@github-actions github-actions 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
@mathlib-dependent-issues mathlib-dependent-issues bot added the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Mar 25, 2026
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@mike1729 mike1729 marked this pull request as draft March 25, 2026 18:32
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mathlib-bors bot commented Mar 25, 2026

This pull request is now in draft mode. No active bors state needed cleanup.

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