Theorems · Theorem · general topology
Complex.subfield_eq_of_closed
∀ {K : Subfield ℂ}, IsClosed ↑K → K = Complex.ofRealHom.fieldRange ∨ K = ⊤The only closed subfields of ℂ are ℝ and ℂ.
- Defined in
- Mathlib.Topology.Instances.Complex
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Set.imageproof · cited by 5,609
- Complexstatement and proof · cited by 5,565
- Bot.botproof · cited by 4,720
- Set.rangeproof · cited by 4,705
- le_reflproof · cited by 2,061
- Complex.ofRealproof · cited by 1,654
- IsClosedstatement and proof · cited by 1,639
- closureproof · cited by 1,254
Cited by2
Results whose statement or proof uses this declaration.
- Complex.uniformContinuous_ringHom_eq_id_or_conjproof · cited by 1