Theorems · Theorem · functional analysis
tendsto_norm_atTop_iff_cobounded
∀ {α : Type u_1} {E : Type u_2} [inst : SeminormedAddGroup E] {f : α → E} {l : Filter α},
Filter.Tendsto (fun x => ‖f x‖) l Filter.atTop ↔ Filter.Tendsto f l (Bornology.cobounded E)- Defined in
- Mathlib.Analysis.Normed.Group.Bounded
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Filterstatement and proof · cited by 8,121
- Norm.normstatement and proof · cited by 5,413
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- SeminormedAddGroupstatement and proof · cited by 331
- Bornology.coboundedstatement · cited by 162
- Filter.tendsto_comap_iffproof · cited by 55
- comap_norm_atTopproof · cited by 4
Cited by13
Results whose statement or proof uses this declaration.
- tendsto_norm_cobounded_atTopproof · cited by 11
- tendsto_intCast_atBot_sup_atTop_coboundedproof · cited by 2
- RCLike.tendsto_ofReal_atTop_coboundedproof · cited by 2
- tangentConeAt.lim_zeroproof · cited by 1
- Polynomial.isProperMap_evalproof · cited by 1
- tendsto_natCast_atTop_coboundedproof · cited by 1
- tendsto_nhds_iff_meromorphicOrderAt_nonnegproof · cited by 1
- NormedAlgebra.Real.exists_isMonicOfDegree_two_and_aeval_eq_zeroproof · cited by 1
- HasFDerivAt.limproof · cited by 1
- tendsto_zero_iff_meromorphicOrderAt_posproof · cited by 0
- RCLike.tendsto_ofReal_atBot_coboundedproof · cited by 0
- RCLike.tendsto_ofReal_cobounded_coboundedproof · cited by 0