Mathlib Map

Theorems · Theorem · functional analysis

GeneralSchauderBasis.proj_empty

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {X : Type u_2} [inst_1 : NormedAddCommGroup X]
  [inst_2 : NormedSpace 𝕜 X] {β : Type u_3} {L : SummationFilter β} (b : GeneralSchauderBasis β 𝕜 X L), b.proj ∅ = 0

The projection on the empty set is the zero map.

Defined in
Mathlib.Analysis.Normed.Module.Bases
Cited by
2 results in Mathlib
Foundations
Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpace
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Around this declaration

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

UnconditionalSchauderBasis.bddAbove_range_nnnorm_proj · cited by 1UnconditionalSchauderBasi…SchauderBasis.proj_zero · cited by 1SchauderBasis.proj_zeroRingHom.id · cited by 18349RingHom.idNormedAddCommGroup · cited by 15752NormedAddCommGroupFinset · cited by 13712FinsetNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldContinuousLinearMap · cited by 5352ContinuousLinearMapSummationFilter · cited by 607SummationFilterGeneralSchauderBasis · cited by 16GeneralSchauderBasisGeneralSchauderBasis.proj · cited by 15GeneralSchauderBasis.projGeneralSchauderBasis.proj_emp…CITED BYCITES

Cites9

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Cited by2

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