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[Merged by Bors] - fix: don't change bornology with PseudoMetricSpace.replaceUniformity #5330

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This fixes PseudoMetricSpace.replaceUniformity so that it no longer silently changes the bornology. Before the fix, the following example fails, but afterwards, it succeeds.

example {α} [U : UniformSpace α] (m : PseudoMetricSpace α)
    (H : 𝓤[U] = 𝓤[PseudoEMetricSpace.toUniformSpace]) :
  (PseudoMetricSpace.replaceUniformity m H).toBornology = m.toBornology := rfl

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@j-loreaux j-loreaux added awaiting-review The author would like community review of the PR easy < 20s of review time. See the lifecycle page for guidelines. awaiting-CI labels Jun 21, 2023
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Should that example by added to guard against a future change breaking the definitional equality? Happy if that doesn't seem necessary to you.

bors d+

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bors bot commented Jun 23, 2023

✌️ j-loreaux can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@github-actions github-actions bot added delegated and removed awaiting-review The author would like community review of the PR labels Jun 23, 2023
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bors merge

bors bot pushed a commit that referenced this pull request Jun 23, 2023
#5330)

This fixes `PseudoMetricSpace.replaceUniformity` so that it no longer silently changes the bornology. Before the fix, the following example fails, but afterwards, it succeeds.

```lean
example {α} [U : UniformSpace α] (m : PseudoMetricSpace α)
    (H : 𝓤[U] = 𝓤[PseudoEMetricSpace.toUniformSpace]) :
  (PseudoMetricSpace.replaceUniformity m H).toBornology = m.toBornology := rfl
```
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bors bot commented Jun 23, 2023

Pull request successfully merged into master.

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@bors bors bot changed the title fix: don't change bornology with PseudoMetricSpace.replaceUniformity [Merged by Bors] - fix: don't change bornology with PseudoMetricSpace.replaceUniformity Jun 23, 2023
@bors bors bot closed this Jun 23, 2023
@bors bors bot deleted the j-loreaux/fix-replaceUniformity branch June 23, 2023 18:07
semorrison pushed a commit that referenced this pull request Jun 25, 2023
#5330)

This fixes `PseudoMetricSpace.replaceUniformity` so that it no longer silently changes the bornology. Before the fix, the following example fails, but afterwards, it succeeds.

```lean
example {α} [U : UniformSpace α] (m : PseudoMetricSpace α)
    (H : 𝓤[U] = 𝓤[PseudoEMetricSpace.toUniformSpace]) :
  (PseudoMetricSpace.replaceUniformity m H).toBornology = m.toBornology := rfl
```
semorrison pushed a commit that referenced this pull request Jun 28, 2023
#5330)

This fixes `PseudoMetricSpace.replaceUniformity` so that it no longer silently changes the bornology. Before the fix, the following example fails, but afterwards, it succeeds.

```lean
example {α} [U : UniformSpace α] (m : PseudoMetricSpace α)
    (H : 𝓤[U] = 𝓤[PseudoEMetricSpace.toUniformSpace]) :
  (PseudoMetricSpace.replaceUniformity m H).toBornology = m.toBornology := rfl
```
kbuzzard pushed a commit that referenced this pull request Jul 6, 2023
#5330)

This fixes `PseudoMetricSpace.replaceUniformity` so that it no longer silently changes the bornology. Before the fix, the following example fails, but afterwards, it succeeds.

```lean
example {α} [U : UniformSpace α] (m : PseudoMetricSpace α)
    (H : 𝓤[U] = 𝓤[PseudoEMetricSpace.toUniformSpace]) :
  (PseudoMetricSpace.replaceUniformity m H).toBornology = m.toBornology := rfl
```
bors bot pushed a commit that referenced this pull request Aug 22, 2023
This shows that C⋆-algebras are always `RegularNormedAlgebra`s, so that their `Unitization` is equipped with a norm. Moreover, we show this norm is a C⋆-norm.

- [x] depends on: #5330
- [x] depends on: #5741
- [x] depends on: #5742 
- [x] depends on: #5743
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