Theorems · Theorem · general topology
Function.Periodic.isBounded_of_continuous
∀ {α : Type u} [inst : PseudoMetricSpace α] {f : ℝ → α} {c : ℝ},
Function.Periodic f c → c ≠ 0 → Continuous f → Bornology.IsBounded (Set.range f)A continuous, periodic function is bounded.
- Defined in
- Mathlib.Topology.Instances.Real.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Set.rangestatement · cited by 4,705
- Continuousstatement and proof · cited by 2,592
- PseudoMetricSpacestatement and proof · cited by 1,550
- Bornology.IsBoundedstatement · cited by 293
- Function.Periodicstatement and proof · cited by 154
- IsCompact.isBoundedproof · cited by 29
- Function.Periodic.compact_of_continuousproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.