Theorems · Theorem · functional analysis
ContinuousMap.rclikeToReal_apply
∀ {X : Type u_1} {𝕜 : Type u_2} [inst : TopologicalSpace X] [inst_1 : RCLike 𝕜] (f : C(X, 𝕜)) (x : X),
f.rclikeToReal x = RCLike.re (f x)- Defined in
- Mathlib.Analysis.RCLike.ContinuousMap
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 171 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.
Cites9
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 · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- ContinuousMapstatement and proof · cited by 2,491
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement · cited by 319
- ContinuousMap.rclikeToRealstatement and proof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- ContinuousMap.IsSelfAdjoint.realToRCLike_rclikeToRealproof · cited by 1
- ContinuousMap.rclikeToReal_monotoneproof · cited by 0
- ContinuousMap.rclikeToReal_realToRCLikeproof · cited by 0