Theorems · Theorem · functional analysis
ContinuousMap.IsSelfAdjoint.realToRCLike_rclikeToReal
∀ {X : Type u_1} {𝕜 : Type u_2} [inst : TopologicalSpace X] [inst_1 : RCLike 𝕜] {f : C(X, 𝕜)},
IsSelfAdjoint f → ContinuousMap.realToRCLike 𝕜 f.rclikeToReal = f- Defined in
- Mathlib.Analysis.RCLike.ContinuousMap
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 172 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- RCLikestatement and proof · cited by 2,829
- ContinuousMapstatement and proof · cited by 2,491
- Star.starproof · cited by 1,082
- starRingEndproof · cited by 671
- IsSelfAdjointstatement and proof · cited by 545
- RCLike.ofRealproof · cited by 350
- ContinuousMap.extproof · cited by 92
- IsSelfAdjoint.star_eqproof · cited by 58
- ContinuousMap.realToRCLikestatement · cited by 18
- ContinuousMap.rclikeToRealstatement and proof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousMap.range_realToRCLike_eq_isSelfAdjointproof · cited by 0