Theorems · Definition · general topology
preCantorSet
ℕ → Set ℝ
The order n pre-Cantor set, defined starting from [0, 1] and successively removing the
middle third of each interval. Formally, the order n + 1 pre-Cantor set is the
union of the images under the functions (· / 3) and ((2 + ·) / 3) of preCantorSet n.
- Defined in
- Mathlib.Topology.Instances.CantorSet
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by13
Results whose statement or proof uses this declaration.
- cantorSetproof · cited by 14
- cantorSet_subset_unitIntervalproof · cited by 3
- ofDigits_zero_two_sequence_mem_cantorSetproof · cited by 2
- preCantorSet_antitonestatement and proof · cited by 2
- quarter_mem_preCantorSetstatement · cited by 1
- quarters_mem_preCantorSetstatement and proof · cited by 1
- cantorSet_eq_union_halvesproof · cited by 1
- isClosed_preCantorSetstatement and proof · cited by 1
- preCantorSet_zerostatement · cited by 1
- preCantorSet.eq_defstatement and proof · cited by 0
- preCantorSet_subset_unitIntervalstatement and proof · cited by 0
- preCantorSet_succstatement · cited by 0