[Merged by Bors] - feat(analysis/normed_space/add_torsor_bases): barycentric coordinates are open maps (in finite dimensions over a complete field) #9543
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… are open maps (in finite dimensions over a complete field) Formalized as part of the Sphere Eversion project.
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| let w : ι → k := λ j', if j' = i then x else 1-x, | ||
| have hw : s.sum w = 1, { simp [hij, finset.sum_ite, finset.filter_insert, finset.filter_eq'], }, | ||
| use s.affine_combination p w, | ||
| simp only [barycentric_coord_apply_combination_of_mem h_ind h_tot hi hw, ite_eq_left_iff, |
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| simp only [barycentric_coord_apply_combination_of_mem h_ind h_tot hi hw, ite_eq_left_iff, |
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… are open maps (in finite dimensions over a complete field) (#9543) Using the open mapping theorem with a one-dimensional codomain feels a bit ridiculous but I see no reason not to do so. Formalized as part of the Sphere Eversion project.
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Using the open mapping theorem with a one-dimensional codomain feels a bit ridiculous but I see no reason not to do so.
Formalized as part of the Sphere Eversion project.