Theorems · Theorem · functional analysis
ContinuousMap.realToRCLike_apply
∀ {X : Type u_1} (𝕜 : Type u_2) [inst : TopologicalSpace X] [inst_1 : RCLike 𝕜] (f : C(X, ℝ)) (x : X),
(ContinuousMap.realToRCLike 𝕜 f) x = ↑(f x)- Defined in
- Mathlib.Analysis.RCLike.ContinuousMap
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 161 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.
Cites7
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
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- RCLikestatement and proof · cited by 2,829
- ContinuousMapstatement and proof · cited by 2,491
- RCLike.ofRealstatement · cited by 350
- ContinuousMap.realToRCLikestatement and proof · cited by 18
Cited by5
Results whose statement or proof uses this declaration.
- ContinuousMap.IsSelfAdjoint.realToRCLike_rclikeToRealproof · cited by 1
- ContinuousMap.isometry_realToRCLikeproof · cited by 0
- ContinuousMap.isSelfAdjoint_realToRCLikeproof · cited by 0
- ContinuousMap.rclikeToReal_realToRCLikeproof · cited by 0
- ContinuousMap.spectrum_realToRCLikeproof · cited by 0