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Theorems · Theorem · geometry

Projectivization.Subspace.span_empty

∀ {K : Type u_1} {V : Type u_2} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V],
  Projectivization.Subspace.span ∅ = ⊥

The span of the empty set is the bottom of the lattice of subspaces.

Defined in
Mathlib.LinearAlgebra.Projectivization.Subspace
Cited by
0 results in Mathlib
Foundations
Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DivisionRingAddCommGroupModule
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Set · cited by 53352SetModule · cited by 20661ModuleAddCommGroup · cited by 12871AddCommGroupBot.bot · cited by 4720Bot.botDivisionRing · cited by 1062DivisionRingGaloisInsertion.gc · cited by 137GaloisInsertion.gcProjectivization · cited by 111ProjectivizationGaloisConnection.l_bot · cited by 63GaloisConnection.l_botProjectivization.Subspace · cited by 34Projectivization.SubspaceProjectivization.Subspace.span · cited by 16Subspace.spanProjectivization.Subspace.gi · cited by 7Subspace.giSubspace.span_emptyCITED BYCITES

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