Theorems · Theorem · field theory
AbsoluteValue.IsEquiv.equivWithAbs_image_mem_nhds_zero
∀ {F : Type u_1} [inst : Field F] {v w : AbsoluteValue F ℝ},
v.IsEquiv w → ∀ {U : Set (WithAbs v)}, U ∈ nhds 0 → ⇑(WithAbs.congr v w (RingEquiv.refl F)) '' U ∈ nhds 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Filterstatement · cited by 8,121
- Fieldstatement and proof · cited by 7,404
- Set.imagestatement and proof · cited by 5,609
- nhdsstatement and proof · cited by 5,554
- LT.lt.leproof · cited by 2,189
- RingEquivstatement · cited by 1,147
- Metric.ballproof · cited by 735
- RingEquiv.symmproof · cited by 567
- Set.mem_image_of_memproof · cited by 371
Cited by1
Results whose statement or proof uses this declaration.
- AbsoluteValue.IsEquiv.isEmbedding_equivWithAbsproof · cited by 1