Theorems · Theorem · functional analysis

Filter.Tendsto.isVonNBounded_range

∀ (𝕜 : Type u_1) {E : Type u_3} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
  [inst_3 : TopologicalSpace E] [IsTopologicalAddGroup E] [ContinuousSMul 𝕜 E] {f : ℕ → E} {x : E},
  Filter.Tendsto f Filter.atTop (nhds x) → Bornology.IsVonNBounded 𝕜 (Set.range f)

Defined in: Mathlib.Analysis.LocallyConvex.Bounded
Cited by: 1 results in Mathlib
Foundations: Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedField AddCommGroup Module TopologicalSpace IsTopologicalAddGroup ContinuousSMul

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Cites14

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
Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
nhdsstatement and proof · cited by 5,554
Set.rangestatement · cited by 4,705
Filter.Tendstostatement and proof · cited by 3,814
Filter.atTopstatement and proof · cited by 2,405
IsTopologicalAddGroupstatement and proof · cited by 1,394
NormedFieldstatement and proof · cited by 1,084
ContinuousSMulstatement and proof · cited by 1,016
Bornology.IsVonNBoundedstatement · cited by 136
Filter.Tendsto.cauchySeqproof · cited by 20

Cited by1

Results whose statement or proof uses this declaration.

LinearMap.continuousAt_zero_of_locally_boundedproof · cited by 1