Theorems · Theorem · complex analysis
Complex.ringHom_eq_ofReal_of_continuous
∀ {f : ℝ →+* ℂ}, Continuous ⇑f → f = Complex.ofRealHomThe only continuous ring homomorphism from ℝ to ℂ is the identity.
- 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.
Cites10
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
- Realstatement and proof · cited by 25,697
- RingHomstatement and proof · cited by 10,189
- Complexstatement and proof · cited by 5,565
- Continuousstatement and proof · cited by 2,592
- AlgHom.toRingHomproof · cited by 490
- Algebra.ofIdproof · cited by 166
- Complex.ofRealHomstatement and proof · cited by 21
- AlgHom.mk'proof · cited by 5
- map_real_smulproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Complex.uniformContinuous_ringHom_eq_id_or_conjproof · cited by 1