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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
Assumes
SemifieldLinearOrderIsStrictOrderedRingTopologicalSpaceOrderTopology

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Filter.Tendsto.inv_tendsto_atTop · cited by 21Tendsto.inv_tendsto_atToptendsto_pow_atTop_nhds_zero_of_lt_one · cited by 18tendsto_pow_atTop_nhds_ze…Filter.Tendsto.div_atTop · cited by 12Tendsto.div_atTopComplex.tendsto_mul_log_one_add_of_tendsto · cited by 3Complex.tendsto_mul_log_o…PhragmenLindelof.horizontal_strip · cited by 3PhragmenLindelof.horizont…tendsto_nat_ceil_mul_div_atTop · cited by 2tendsto_nat_ceil_mul_div_…Real.tendsto_exp_neg_atTop_nhds_zero · cited by 2Real.tendsto_exp_neg_atTo…CircleDeg1Lift.tendsto_translationNumber_of_dist_bounded_aux · cited by 2CircleDeg1Lift.tendsto_tr…qExpansion_coeff_isBigO_of_norm_isBigO · cited by 2qExpansion_coeff_isBigO_o…ProbabilityTheory.tendsto_charFun_inv_sqrt_mul_pow · cited by 1ProbabilityTheory.tendsto…tendsto_mul_add_inv_atTop_nhds_zero · cited by 1tendsto_mul_add_inv_atTop…Asymptotics.IsLittleO.of_tendsto_div_atTop · cited by 1IsLittleO.of_tendsto_div_…Real.tendsto_pow_mul_exp_neg_atTop_nhds_zero · cited by 1Real.tendsto_pow_mul_exp_…Circle.hasBasis_centeredArc_div_two_pow · cited by 1Circle.hasBasis_centeredA…NNRat.tendsto_inv_atTop_nhds_zero_nat · cited by 1NNRat.tendsto_inv_atTop_n…TopologicalSpace · cited by 24529TopologicalSpaceLinearOrder · cited by 8572LinearOrdernhds · cited by 5554nhdsFilter.Tendsto · cited by 3814Filter.TendstoIsStrictOrderedRing · cited by 2490IsStrictOrderedRingFilter.atTop · cited by 2405Filter.atTopOrderTopology · cited by 1355OrderTopologySemifield · cited by 439Semifieldinf_le_left · cited by 286inf_le_leftFilter.Tendsto.mono_right · cited by 53Tendsto.mono_righttendsto_inv_atTop_nhdsGT_zero · cited by 2tendsto_inv_atTop_nhdsGT_…tendsto_inv_atTop_zeroCITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by19

Results whose statement or proof uses this declaration.