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fix(topology/metric_space): fix uniform structure on Pi types #1551

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merged 5 commits into from
Oct 17, 2019

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The uniform structure induced from a metric space structure on a Pi type is currently not defeq to the product uniform structure. This is fixed in this PR. Before the PR,

lemma diamond {n : ℕ} : is_open (pi (univ : set (fin n)) (λi, (univ : set ℝ))) :=
begin
  have A : finite (univ : set (fin n)) := finite_univ,
  have B : ∀i : fin n, i ∈ univ → is_open (univ : set ℝ) := λi hi, is_open_univ,
  convert is_open_set_pi A B,
end

leaves the goal uniform_space.to_topological_space (fin n → ℝ) = Pi.topological_space. After the PR, there is no goal left.

@sgouezel sgouezel added the awaiting-review The author would like community review of the PR label Oct 15, 2019
@PatrickMassot PatrickMassot added ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) and removed awaiting-review The author would like community review of the PR labels Oct 17, 2019
@mergify mergify bot merged commit 905beb0 into leanprover-community:master Oct 17, 2019
@sgouezel sgouezel deleted the pi_topology branch December 2, 2019 10:38
anrddh pushed a commit to anrddh/mathlib that referenced this pull request May 15, 2020
…over-community#1551)

* fix(topology/metric_space): fix uniform structure on pi tpype

* cleanup

* better construction of metric from emetric

* use simp only instead of simp
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3 participants