[Merged by Bors] - feat(topology/algebra/group): added (right/left)_coset_(open/closed) #11876
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Sebastian-Monnet
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kbuzzard
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ocfnash
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src/topology/algebra/group.lean
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| @@ -67,10 +67,18 @@ by { ext, refl } | |||
| lemma is_open_map_mul_left (a : G) : is_open_map (λ x, a * x) := | |||
| (homeomorph.mul_left a).is_open_map | |||
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| @[to_additive is_open.left_add_coset] | |||
| lemma is_open.left_coset {U : set G} (x : G) (h : is_open U) : is_open (left_coset x U) := | |||
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I think you need to swap the order of the arguments for dot notation to work:
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| lemma is_open.left_coset {U : set G} (x : G) (h : is_open U) : is_open (left_coset x U) := | |
| lemma is_open.left_coset {U : set G} (h : is_open U) (x : G) : is_open (left_coset x U) := |
and likewise with the other lemmas below
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Dot notation doesn't care about the argument order here, the original was fine
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I think it does matter in some situations. For example the following:
example {U : set G} (h : is_open U) : ∀ x, is_open (left_coset x U) := h.left_cosetonly works when is_open.left_coset is defined with x following h.
I admit that the ordering does not matter for something of the form:
example {U : set G} (h : is_open U) (x : G) : is_open (left_coset x U) := h.left_coset xwhich is likely to be the more typical usage.
I'm happy to be corrected if there's more to it!
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…11876) Added lemmas saying that, in a topological group, cosets of an open (resp. closed) set are open (resp. closed).
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Added lemmas saying that, in a topological group, cosets of an open (resp. closed) set are open (resp. closed).