Theorems · Theorem · complex analysis
Complex.ringHom_eq_id_or_conj_of_continuous
∀ {f : ℂ →+* ℂ}, Continuous ⇑f → f = RingHom.id ℂ ∨ f = starRingEnd ℂThe only continuous ring homomorphisms from ℂ to ℂ are the identity and the complex
conjugation.
- Defined in
- Mathlib.Analysis.Complex.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
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
- RingHom.idstatement · cited by 18,349
- RingHomstatement and proof · cited by 10,189
- Complexstatement and proof · cited by 5,565
- Continuousstatement and proof · cited by 2,592
- starRingEndstatement · cited by 671
- AlgHom.mk'proof · cited by 5
- map_real_smulproof · cited by 2
- Complex.real_algHom_eq_id_or_conjproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Complex.uniformContinuous_ringHom_eq_id_or_conjproof · cited by 1