Mathlib Map

Theorems · Definition · functional analysis

RCLike.reCLM

{K : Type u_1} → [inst : RCLike K] → StrongDual ℝ K

The real part in an RCLike field, as a continuous linear map.

Defined in
Mathlib.Analysis.RCLike.Basic
Cited by
20 results in Mathlib
Foundations
Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RCLike
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

StrongDual.extendRCLikeₗ · cited by 17StrongDual.extendRCLikeₗRCLike.continuous_re · cited by 10RCLike.continuous_reintegral_re · cited by 7integral_recontDiff_norm_sq · cited by 5contDiff_norm_sqContinuousMap.starSubalgebra_topologicalClosure_eq_top_of_separatesPoints · cited by 4ContinuousMap.starSubalge…RCLike.hasSum_re · cited by 3RCLike.hasSum_reContinuousLinearMap.reApplyInnerSelf_continuous · cited by 2ContinuousLinearMap.reApp…RCLike.hasSum_ofReal · cited by 2RCLike.hasSum_ofRealConvex.toWeakSpace_closure · cited by 2Convex.toWeakSpace_closureRCLike.re_tsum · cited by 1RCLike.re_tsumRCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict · cited by 1RCLike.restrict_toContinu…RCLike.summable_ofReal · cited by 1RCLike.summable_ofRealLowerSemicontinuousOn.isClosed_re_epigraph · cited by 1LowerSemicontinuousOn.isC…intervalIntegral.intervalIntegral_re · cited by 0intervalIntegral.interval…RCLike.map_to_real · cited by 0RCLike.map_to_realReal · cited by 25697RealRCLike · cited by 2829RCLikeStrongDual · cited by 459StrongDualLinearMap.mkContinuous · cited by 9LinearMap.mkContinuousRCLike.reLm · cited by 6RCLike.reLmRCLike.reCLMCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by21

Results whose statement or proof uses this declaration.