Theorems · Theorem · field theory
krullTopology_mem_nhds_one_iff
∀ (K : Type u_1) (L : Type u_2) [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] (s : Set Gal(L/K)), s ∈ nhds 1 ↔ ∃ E, FiniteDimensional K ↥E ∧ ↑E.fixingSubgroup ⊆ s
- Defined in
- Mathlib.FieldTheory.KrullTopology
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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 and proof · cited by 8,121
- Fieldstatement and proof · cited by 7,404
- nhdsstatement · cited by 5,554
- Subgroupstatement and proof · cited by 3,593
- FiniteDimensionalstatement and proof · cited by 1,854
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement and proof · cited by 988
- Subsemigroup.carrierproof · cited by 160
- Submonoid.toSubsemigroupproof · cited by 159
Cited by2
Results whose statement or proof uses this declaration.
- InfiniteGalois.restrictNormalHom_continuousproof · cited by 1
- krullTopology_mem_nhds_one_iff_of_normalproof · cited by 1