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Theorems · Theorem · algebraic topology

Bundle.Trivial.symmL_trivialization

∀ (𝕜 : Type u_1) (B : Type u_2) (F : Type u_3) [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] [inst_3 : TopologicalSpace B] (x : B),
  Bundle.Trivialization.symmL 𝕜 (Bundle.Trivial.trivialization B F) x = ContinuousLinearMap.id 𝕜 F
Defined in
Mathlib.Topology.VectorBundle.Constructions
Cited by
1 results in Mathlib
Foundations
Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Bundle.Trivialization.contMDiffAt_symmL · cited by 1Trivialization.contMDiffA…TopologicalSpace · cited by 24529TopologicalSpaceRingHom.id · cited by 18349RingHom.idNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldContinuousLinearMap · cited by 5352ContinuousLinearMapContinuousLinearMap.ext · cited by 320ContinuousLinearMap.extContinuousLinearMap.id · cited by 233ContinuousLinearMap.idBundle.Trivialization.symmL · cited by 32Trivialization.symmLBundle.Trivial · cited by 20Bundle.TrivialBundle.Trivial.trivialization · cited by 17Trivial.trivializationBundle.Trivialization.symmL_apply · cited by 13Trivialization.symmL_applyBundle.Trivial.trivialization_baseSet · cited by 3Trivial.trivialization_ba…Bundle.Trivial.trivialization_symm_apply · cited by 2Trivial.trivialization_sy…Trivial.symmL_trivializationCITED BYCITES

Cites14

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Cited by1

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