Theorems · Theorem · field theory
tendsto_inv_atBot_zero
∀ {𝕜 : Type u_1} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] [inst_3 : TopologicalSpace 𝕜]
[OrderTopology 𝕜], Filter.Tendsto (fun r => r⁻¹) Filter.atBot (nhds 0)- Defined in
- Mathlib.Topology.Algebra.Order.Field
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 82 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
- OrderTopologystatement and proof · cited by 1,355
- Filter.atBotstatement · cited by 512
- inf_le_leftproof · cited by 286
- Filter.Tendsto.mono_rightproof · cited by 53
- tendsto_inv_atBot_nhdsLT_zeroproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- tendsto_mul_add_inv_atTop_nhds_zeroproof · cited by 1
- Filter.Tendsto.div_atBotproof · cited by 1
- Filter.Tendsto.inv_tendsto_atBotproof · cited by 0