Theorems · Theorem · functional analysis
FiniteDimensional.proper_rclike
∀ (K : Type u_1) (E : Type u_2) [inst : RCLike K] [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace K E] [FiniteDimensional K E], ProperSpace E
A finite-dimensional vector space over an RCLike is a proper metric space.
This is not an instance because it would cause a search for FiniteDimensional ?x E before
RCLike ?x.
- Defined in
- Mathlib.Analysis.RCLike.Lemmas
- 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- RCLikestatement and proof · cited by 2,829
- FiniteDimensionalstatement and proof · cited by 1,854
- ProperSpacestatement · cited by 190
- NormedSpace.restrictScalarsproof · cited by 39
- FiniteDimensional.transproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- HasCompactSupport.hasFDerivAt_convolution_rightproof · cited by 2
- LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensionalproof · cited by 1
- LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensionalproof · cited by 0