Theorems · Theorem · functional analysis
isOpen_setOf_linearIndependent
Deprecated since 2026-07-09Use isOpen_setOfPred_linearIndependent instead.
∀ {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}Alias of isOpen_setOfPred_linearIndependent.
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- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement · cited by 15,752
- NormedSpacestatement · cited by 12,499
- NontriviallyNormedFieldstatement · cited by 8,742
- Set.ofPredstatement · cited by 6,101
- Finitestatement · cited by 3,029
- CompleteSpacestatement · cited by 2,532
- IsOpenstatement · cited by 2,400
- LinearIndependentstatement · cited by 560
- isOpen_setOfPred_linearIndependentproof · cited by 3
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