Theorems · Theorem · general topology
PolishSpace.exists_nat_nat_continuous_surjective
∀ (α : Type u_3) [inst : TopologicalSpace α] [PolishSpace α] [Nonempty α], ∃ f, Continuous f ∧ Function.Surjective f
Any nonempty Polish space is the continuous image of the fundamental space ℕ → ℕ.
- Defined in
- Mathlib.Topology.MetricSpace.Polish
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement · cited by 2,592
- PolishSpacestatement and proof · cited by 57
- exists_nat_nat_continuous_surjective_of_completeSpaceproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.analyticSet_range_of_polishSpaceproof · cited by 6