Theorems · Theorem · general topology
polynomialFunctions.starClosure_topologicalClosure
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] (s : Set 𝕜) [inst_1 : CompactSpace ↑s],
(polynomialFunctions s).starClosure.topologicalClosure = ⊤The star subalgebra generated by polynomials functions is dense in C(s, 𝕜) when s is
compact and 𝕜 is either ℝ or ℂ.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLikeCompactSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Top.topstatement · cited by 9,680
- Set.Elemstatement and proof · cited by 7,166
- RCLikestatement and proof · cited by 2,829
- ContinuousMapstatement · cited by 2,491
- CompactSpacestatement and proof · cited by 593
- le_sup_leftproof · cited by 265
- StarSubalgebrastatement · cited by 194
- StarSubalgebra.toSubalgebraproof · cited by 58
- StarSubalgebra.topologicalClosurestatement · cited by 22
- polynomialFunctionsstatement and proof · cited by 16
- Subalgebra.starClosurestatement and proof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- ContinuousMap.elemental_id_eq_topproof · cited by 2
- ContinuousMap.induction_on_of_compactproof · cited by 2
- ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_idproof · cited by 1
- ContinuousMap.starAlgHom_ext_map_Xproof · cited by 0