Theorems · Theorem · general topology
PolishSpace.iInf
∀ {α : Type u_1} {ι : Type u_3} [Countable ι] {t : ι → TopologicalSpace α},
(∃ i₀, ∀ (i : ι), t i ≤ t i₀) → (∀ (i : ι), PolishSpace α) → PolishSpace α- Defined in
- Mathlib.Topology.MetricSpace.Polish
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Countable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- CompleteSpaceproof · cited by 2,532
- UniformSpaceproof · cited by 2,040
- iInfstatement and proof · cited by 1,690
- uniformityproof · cited by 765
- SecondCountableTopologyproof · cited by 750
- Countablestatement and proof · cited by 633
- T1Spaceproof · cited by 275
- Filter.IsCountablyGeneratedproof · cited by 220
- iInf_leproof · cited by 104
- PolishSpacestatement and proof · cited by 57
- CompletePseudometrizable.iInfproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- PolishSpace.exists_polishSpace_forall_leproof · cited by 2