Theorems · Definition · functional analysis
ContinuousLinearMap.id
(R₁ : Type u_1) →
[inst : Semiring R₁] →
(M₁ : Type u_4) →
[inst_1 : TopologicalSpace M₁] → [inst_2 : AddCommMonoid M₁] → [inst_3 : Module R₁ M₁] → M₁ →L[R₁] M₁the identity map as a continuous linear map.
- Cited by
- 233 results in Mathlib
- Foundations
- Depth 18 from the axioms, rests on 174 definitions · uses no axioms
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.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- ContinuousLinearMapstatement · cited by 5,352
- LinearMap.idproof · cited by 625
- continuous_idproof · cited by 192
Cited by247
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.inrproof · cited by 59
- ContinuousLinearMap.inlproof · cited by 39
- analyticAt_idproof · cited by 39
- MeasureTheory.weightedSMulproof · cited by 31
- ContinuousLinearMap.applyproof · cited by 23
- ContinuousLinearMap.comp_idstatement · cited by 21
- hasFDerivAt_idstatement · cited by 18
- ContinuousLinearMap.id_compstatement · cited by 16
- ContinuousAlternatingMap.fderivCompContinuousLinearMapproof · cited by 13
- hasFDerivWithinAt_idstatement · cited by 11
- ContinuousLinearMap.norm_toSpanSingletonproof · cited by 11
- hasStrictFDerivAt_idstatement · cited by 11
Showing the 200 most cited of 247.