Theorems · Theorem · field theory
tendsto_const_mul_zpow_atTop_zero
∀ {𝕜 : Type u_1} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] [inst_3 : TopologicalSpace 𝕜]
[OrderTopology 𝕜] {n : ℤ} {c : 𝕜}, n < 0 → Filter.Tendsto (fun x => c * x ^ n) Filter.atTop (nhds 0)- Defined in
- Mathlib.Topology.Algebra.Order.Field
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Filter.atTopstatement · cited by 2,405
- MulZeroClass.mul_zeroproof · cited by 2,091
- OrderTopologystatement and proof · cited by 1,355
- Filter.Tendsto.const_mulproof · cited by 55
- tendsto_zpow_atTop_zeroproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_const_mul_zpow_atTop_nhds_iffproof · cited by 1