[Merged by Bors] - feat(topology/uniform_space): some basic lemmas #3123
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| @@ -461,6 +502,25 @@ lemma ball_eq_of_symmetry {V : set (β × β)} (hV : symmetric_rel V) {x} : | |||
| ball x V = {y | (y, x) ∈ V} := | |||
| by { ext y, rw mem_ball_symmetry hV, exact iff.rfl } | |||
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| lemma mem_comp_of_mem_ball {V W : set (β × β)} {x y z : β} (hV : symmetric_rel V) | |||
| (hx : x ∈ ball z V) (hy : y ∈ ball z W) : (x, y) ∈ V ○ W := | |||
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| (hx : x ∈ ball z V) (hy : y ∈ ball z W) : (x, y) ∈ V ○ W := | |
| (hx : x ∈ ball z V) (hy : y ∈ ball z W) : (x, y) ∈ V ○ W := |
| exact mem_sets_of_superset r_in r_sub, } | ||
| end | ||
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| lemma uniformity_has_basis_closure : has_basis (𝓤 α) (λ V : set (α × α), V ∈ 𝓤 α) closure := |
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A docstring on this one would be welcome, as the has_basis ... closure is surprising at first, before one tries to remember what has_basis really says.
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This is the second PR on the road to Heine. It contains various elementary lemmas about uniform spaces.
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…#3123) This is the second PR on the road to Heine. It contains various elementary lemmas about uniform spaces.
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This is the second PR on the road to Heine. It contains various elementary lemmas about uniform spaces.
This PR is slightly controversial. You won't notice if you only look at the diff, but some of those lemmas are almost duplicating existing lemmas. This is because I'm returning to Bourbaki instead of following Johannes. The main differences are Johannes loves
filter.lift'and he doesn't like symmetric entourages. So some lemmas from this PR are expressed withoutlift'but have the same mathematical content as existing lemmas usinglift'and some lemmas from this PR are symmetric versions of existing lemmas.