Theorems · Theorem · general topology
exists_retractionCantorSet
∀ {X : Set (ℕ → Bool)}, IsClosed X → X.Nonempty → ∃ f, Continuous f ∧ Set.range f = X- Cited by
- 1 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- Set.rangestatement and proof · cited by 4,705
- Set.Nonemptystatement and proof · cited by 2,627
- Continuousstatement · cited by 2,592
- IsClosedstatement and proof · cited by 1,639
- LipschitzWithproof · cited by 316
- LipschitzWith.continuousproof · cited by 30
- PiNat.exists_lipschitz_retraction_of_isClosedproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- exists_nat_bool_continuous_surjective_of_compactproof · cited by 0