Theorems · Theorem · general topology
IsClosed.polishSpace
∀ {α : Type u_1} [inst : TopologicalSpace α] [PolishSpace α] {s : Set α}, IsClosed s → PolishSpace ↑sA closed subset of a Polish space is also Polish.
- Defined in
- Mathlib.Topology.MetricSpace.Polish
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpacePolishSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement · cited by 7,166
- IsClosedstatement and proof · cited by 1,639
- PolishSpacestatement and proof · cited by 57
- IsClosed.isClosedEmbedding_subtypeValproof · cited by 19
- Topology.IsClosedEmbedding.polishSpaceproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- IsClosed.analyticSetproof · cited by 2
- IsClosed.isClopenableproof · cited by 1
- MeasureTheory.measurableEquiv_range_coe_nat_of_infinite_of_countableproof · cited by 1
- IsClosed.measurableSet_image_of_continuousOn_injOnproof · cited by 1
- MeasureTheory.AnalyticSet.iInterproof · cited by 0
- MeasurableSet.standardBorelproof · cited by 0