Theorems · Theorem · functional analysis
Submodule.topologicalClosure_eq_self
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(K : Submodule 𝕜 E) [FiniteDimensional 𝕜 ↥K], K.topologicalClosure = K- Cited by
- 2 results in Mathlib
- Foundations
- Depth 174 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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- FiniteDimensionalstatement and proof · cited by 1,854
- Submodule.topologicalClosurestatement · cited by 50
- Submodule.closed_of_finiteDimensionalproof · cited by 8
- IsClosed.submodule_topologicalClosure_eqproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- LinearMap.orthogonal_kerproof · cited by 2
- ContinuousLinearMap.ker_le_ker_iff_range_le_rangeproof · cited by 0