Theorems · Theorem · functional analysis
isOpen_setOfPred_linearIndependent
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type v} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [CompleteSpace 𝕜] {ι : Type u_1} [Finite ι], IsOpen {f | LinearIndependent 𝕜 f}- Cited by
- 3 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.ofPredstatement · cited by 6,101
- Finitestatement and proof · cited by 3,029
- CompleteSpacestatement and proof · cited by 2,532
- IsOpenstatement · cited by 2,400
- LinearIndependentstatement · cited by 560
- isOpen_iff_mem_nhdsproof · cited by 48
- LinearIndependent.eventuallyproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- isOpen_setOfPred_affineIndependentproof · cited by 1
- isOpen_setOfPred_nat_le_rankproof · cited by 1
- isOpen_setOf_linearIndependentproof · cited by 0