Theorems · Definition · functional analysis
ContinuousAlgEquiv.refl
(R : Type u_1) →
(A : Type u_2) →
[inst : CommSemiring R] → [inst_1 : Semiring A] → [inst_2 : TopologicalSpace A] → [inst_3 : Algebra R A] → A ≃A[R] AThe identity isomorphism as a continuous R-algebra equivalence.
- Defined in
- Mathlib.Topology.Algebra.Algebra.Equiv
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 18 from the axioms · 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
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- AlgEquivproof · cited by 1,681
- continuous_idproof · cited by 192
- ContinuousAlgEquivstatement · cited by 105
- AlgEquiv.reflproof · cited by 50
Cited by32
Results whose statement or proof uses this declaration.
- UpperHalfPlane.σproof · cited by 31
- ModularForm.SL_slash_applyproof · cited by 7
- UpperHalfPlane.gl_smul_eq_self_iff_quadraticproof · cited by 2
- UpperHalfPlane.coe_J_smulproof · cited by 2
- ModularForm.SL_slash_defproof · cited by 2
- SlashInvariantForm.slash_action_eqn'proof · cited by 2
- SlashInvariantForm.vAdd_apply_of_mem_strictPeriodsproof · cited by 2
- UpperHalfPlane.isElliptic_of_exists_smul_eq_selfproof · cited by 1
- UpperHalfPlane.σ_mulproof · cited by 1
- UpperHalfPlane.σ_negproof · cited by 1
- ContinuousAlgEquiv.refl_applystatement · cited by 1
- UpperHalfPlane.smulAux'_improof · cited by 1