Theorems · Theorem · functional analysis
HilbertBasis.dense_span
∀ {ι : Type u_1} {𝕜 : Type u_2} [inst : RCLike 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : InnerProductSpace 𝕜 E] (b : HilbertBasis ι 𝕜 E), (Submodule.span 𝕜 (Set.range ⇑b)).topologicalClosure = ⊤- Cited by
- 1 results in Mathlib
- Foundations
- Depth 236 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- NormedAddCommGroupstatement and proof · cited by 15,752
- Finsetproof · cited by 13,712
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Submodulestatement · cited by 7,192
- Set.rangestatement and proof · cited by 4,705
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Finset.sum_congrproof · cited by 2,323
- Submodule.spanstatement and proof · cited by 1,504
- Filter.Eventually.of_forallproof · cited by 526
Cited by1
Results whose statement or proof uses this declaration.
- HilbertBasis.finite_spans_denseproof · cited by 0