Theorems · Theorem · field theory
tendsto_inv_atTop_zero
∀ {𝕜 : Type u_1} [inst : Semifield 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] [inst_3 : TopologicalSpace 𝕜]
[OrderTopology 𝕜], Filter.Tendsto (fun r => r⁻¹) Filter.atTop (nhds 0)- Defined in
- Mathlib.Topology.Algebra.Order.Field
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 81 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
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Filter.atTopstatement · cited by 2,405
- OrderTopologystatement and proof · cited by 1,355
- Semifieldstatement and proof · cited by 439
- inf_le_leftproof · cited by 286
- Filter.Tendsto.mono_rightproof · cited by 53
- tendsto_inv_atTop_nhdsGT_zeroproof · cited by 2
Cited by19
Results whose statement or proof uses this declaration.
- Filter.Tendsto.inv_tendsto_atTopproof · cited by 21
- tendsto_pow_atTop_nhds_zero_of_lt_oneproof · cited by 18
- Filter.Tendsto.div_atTopproof · cited by 12
- Complex.tendsto_mul_log_one_add_of_tendstoproof · cited by 3
- PhragmenLindelof.horizontal_stripproof · cited by 3
- tendsto_nat_ceil_mul_div_atTopproof · cited by 2
- Real.tendsto_exp_neg_atTop_nhds_zeroproof · cited by 2
- CircleDeg1Lift.tendsto_translationNumber_of_dist_bounded_auxproof · cited by 2
- qExpansion_coeff_isBigO_of_norm_isBigOproof · cited by 2
- ProbabilityTheory.tendsto_charFun_inv_sqrt_mul_powproof · cited by 1
- tendsto_mul_add_inv_atTop_nhds_zeroproof · cited by 1
- Asymptotics.IsLittleO.of_tendsto_div_atTopproof · cited by 1