Theorems · Theorem · field theory
krullTopology_mem_nhds_one_iff_of_normal
∀ (K : Type u_1) (L : Type u_2) [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] [Normal K L] (s : Set Gal(L/K)), s ∈ nhds 1 ↔ ∃ E, FiniteDimensional K ↥E ∧ Normal K ↥E ∧ ↑E.fixingSubgroup ⊆ s
- Defined in
- Mathlib.FieldTheory.KrullTopology
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- SetLike.coestatement and proof · cited by 8,199
- Filterstatement · cited by 8,121
- Fieldstatement and proof · cited by 7,404
- nhdsstatement · cited by 5,554
- Subgroupstatement · cited by 3,593
- FiniteDimensionalstatement and proof · cited by 1,854
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement and proof · cited by 988
- le_transproof · cited by 985
- Normalstatement and proof · cited by 92
Cited by1
Results whose statement or proof uses this declaration.
- InfiniteGalois.krullTopology_mem_nhds_one_iff_of_isGaloisproof · cited by 0