Theorems · Definition · functional analysis
ContinuousMap.realToRCLikeStarAlgHom
(X : Type u_1) → (𝕜 : Type u_2) → [inst : TopologicalSpace X] → [inst_1 : RCLike 𝕜] → C(X, ℝ) →⋆ₐ[ℝ] C(X, 𝕜)
ContinuousMap.realToRCLike as a ⋆-algebra map.
- Defined in
- Mathlib.Analysis.RCLike.ContinuousMap
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceRCLike
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.
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- RCLikestatement and proof · cited by 2,829
- ContinuousMapstatement · cited by 2,491
- StarAlgHomstatement · cited by 215
- RCLike.continuous_ofRealproof · cited by 9
- ContinuousMap.compStarAlgHomproof · cited by 4
- RCLike.ofRealStarAlgHomproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- ContinuousMap.realToRCLike_mulproof · cited by 0
- ContinuousMap.realToRCLikeStarAlgHom_applystatement · cited by 0
- ContinuousMap.realToRCLike_starproof · cited by 0