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Theorems · Theorem · functional analysis

PiTensorProduct.mapL_one

∀ {ι : Type u_1} [inst : Fintype ι] {𝕜 : Type u_2} {E : ι → Type u_3} [inst_1 : (i : ι) → SeminormedAddCommGroup (E i)]
  [inst_2 : NontriviallyNormedField 𝕜] [inst_3 : (i : ι) → NormedSpace 𝕜 (E i)], (PiTensorProduct.mapL fun i => 1) = 1
Defined in
Mathlib.Analysis.Normed.Module.PiTensorProduct.ProjectiveSeminorm
Cited by
0 results in Mathlib
Foundations
Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FintypeSeminormedAddCommGroupNontriviallyNormedFieldNormedSpace
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Around this declaration

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

PiTensorProduct.mapLMonoidHom · cited by 2PiTensorProduct.mapLMonoi…RingHom.id · cited by 18349RingHom.idNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldFintype · cited by 7736FintypeContinuousLinearMap · cited by 5352ContinuousLinearMapSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupPiTensorProduct · cited by 181PiTensorProductPiTensorProduct.mapL · cited by 13PiTensorProduct.mapLPiTensorProduct.mapL_id · cited by 1PiTensorProduct.mapL_idPiTensorProduct.mapL_oneCITED BYCITES

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Cited by1

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