Theorems · Theorem · general topology
Function.Periodic.compact_of_continuous
∀ {α : Type u} [inst : TopologicalSpace α] {f : ℝ → α} {c : ℝ},
Function.Periodic f c → c ≠ 0 → Continuous f → IsCompact (Set.range f)A continuous, periodic function has compact range.
- Defined in
- Mathlib.Topology.Instances.Real.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.rangestatement · cited by 4,705
- Continuousstatement and proof · cited by 2,592
- IsCompactstatement and proof · cited by 1,282
- Function.Periodicstatement and proof · cited by 154
- IsCompact.imageproof · cited by 105
- isCompact_uIccproof · cited by 17
- Function.Periodic.image_uIccproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Function.Periodic.isBounded_of_continuousproof · cited by 0