Theorems · Theorem · functional analysis
MontelSpace.finiteDimensional_of_normedSpace
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [CompleteSpace 𝕜] [hM : MontelSpace 𝕜 E], FiniteDimensional 𝕜 E- Defined in
- Mathlib.Analysis.LocallyConvex.Montel
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- CompleteSpacestatement and proof · cited by 2,532
- FiniteDimensionalstatement · cited by 1,854
- zero_lt_oneproof · cited by 598
- Metric.isClosed_closedBallproof · cited by 28
- NormedSpace.isVonNBounded_closedBallproof · cited by 5
- MontelSpacestatement and proof · cited by 5
- FiniteDimensional.of_isCompact_closedBall₀proof · cited by 2
- MontelSpace.isCompact_of_isClosed_of_isVonNBoundedproof · cited by 1
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