Theorems · Theorem · general topology
cantorSet_eq_union_halves
cantorSet = (fun x => x / 3) '' cantorSet ∪ (fun x => (2 + x) / 3) '' cantorSet
The ternary Cantor set satisfies the equation C = C / 3 ∪ (2 / 3 + C / 3).
- Defined in
- Mathlib.Topology.Instances.CantorSet
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.imagestatement and proof · cited by 5,609
- Set.iInterproof · cited by 1,084
- Function.Bijective.compproof · cited by 26
- Monotone.comp_antitoneproof · cited by 16
- cantorSetstatement · cited by 14
- preCantorSetproof · cited by 12
- Set.monotone_imageproof · cited by 9
- Set.image_iInterproof · cited by 4
- preCantorSet_antitoneproof · cited by 2
- AddGroup.addLeft_bijectiveproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- cantorStep_mem_cantorSetproof · cited by 1