[Merged by Bors] - feat(topology/vector_bundle): define some useful linear maps globally #14484
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src/topology/vector_bundle.lean
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| { cont := by { dsimp, rw [e.coe_linear_map_at b], | ||
| refine continuous_if_const _ (λ hb, _) (λ _, continuous_zero), | ||
| refine continuous_snd.comp (e.to_local_homeomorph.continuous_on.comp_continuous | ||
| (total_space_mk_inducing R F E b).continuous (λ x, e.mem_source.mpr hb)) }, |
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IMHO, this deserves a begin ... end block.
Also, can you explain why you mention (only propositionally equal) in the docstring? At least, I hope that the to_fun fields are defeq?
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No, they are not defeq because the one that is defined everywhere features an if then else. It is defined as if hb : b ∈ e.base_set then e.linear_equiv_at b hb else 0 so it's not defeq to e.linear_equiv_at b hb, it is only propeq to it when `b ∈ e.base_set.
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The real question is whether we really want to keep linear_equiv_at which isn't used anywhere else. Let's keep it for now and remember to delete it if we manage to go as far as jet bundles without ever using it.
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I rebased on master to solve conflicts. |
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bors merge |
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…#14484) * Define `pretrivialization.symmₗ`, `pretrivialization.linear_map_at`, `trivialization.symmL`, `trivialization.continuous_linear_map_at` * These are globally-defined (continuous) linear maps. They are linear equivalences on `e.base_set`, but it is useful to define these globally. They are defined as `0` outside `e.base_set` * These are convenient to define the vector bundle of continuous linear maps. Co-authored-by: Patrick Massot <patrickmassot@free.fr>
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…#14484) * Define `pretrivialization.symmₗ`, `pretrivialization.linear_map_at`, `trivialization.symmL`, `trivialization.continuous_linear_map_at` * These are globally-defined (continuous) linear maps. They are linear equivalences on `e.base_set`, but it is useful to define these globally. They are defined as `0` outside `e.base_set` * These are convenient to define the vector bundle of continuous linear maps. Co-authored-by: Patrick Massot <patrickmassot@free.fr>
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pretrivialization.symmₗ,pretrivialization.linear_map_at,trivialization.symmL,trivialization.continuous_linear_map_ate.base_set, but it is useful to define these globally. They are defined as0outsidee.base_setThis (slightly) conflicts with #14462.
Please merge that PR first, unless this reviews much more easily (branchvb-hom-florishas the merge conflict resolved)