Theorems · Definition · functional analysis
ContinuousLinearEquiv.unitsEquivAut
(R : Type u_1) → [inst : Semiring R] → [inst_1 : TopologicalSpace R] → [ContinuousMul R] → Rˣ ≃ R ≃L[R] R
Continuous linear equivalences R ≃L[R] R are enumerated by Rˣ.
- Defined in
- Mathlib.Topology.Algebra.Module.Equiv
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Equivstatement · cited by 8,337
- Unitsstatement and proof · cited by 2,804
- Units.valproof · cited by 1,966
- ContinuousLinearEquivstatement and proof · cited by 743
- ContinuousLinearEquiv.symmproof · cited by 368
- ContinuousMulstatement and proof · cited by 343
- ContinuousLinearMap.smulRightproof · cited by 126
- ContinuousLinearEquiv.equivOfInverseproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- HasStrictDerivAt.hasStrictFDerivAt_equivstatement · cited by 10
- HasStrictDerivAt.localInverseproof · cited by 7
- HasDerivAt.hasFDerivAt_equivstatement · cited by 2
- AnalyticAt.analyticAt_localInverseproof · cited by 2
- ContinuousLinearEquiv.unitsEquivAut.congr_simpstatement and proof · cited by 0
- ContinuousLinearEquiv.unitsEquivAut_applystatement · cited by 0
- ContinuousLinearEquiv.unitsEquivAut_apply_symmstatement · cited by 0
- ContinuousLinearEquiv.unitsEquivAut_symm_applystatement · cited by 0