Theorems · Theorem · general topology
IsOpen.polishSpace
∀ {α : Type u_3} [inst : TopologicalSpace α] [PolishSpace α] {s : Set α}, IsOpen s → PolishSpace ↑sAn open subset of a Polish space is also Polish.
- Defined in
- Mathlib.Topology.MetricSpace.Polish
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 164 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.
Cites9
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
- SetLike.coeproof · cited by 8,199
- Set.Elemstatement · cited by 7,166
- IsOpenstatement and proof · cited by 2,400
- TopologicalSpace.Opensproof · cited by 2,040
- PolishSpacestatement and proof · cited by 57
- TopologicalSpace.upgradeIsCompletelyMetrizableproof · cited by 7
- TopologicalSpace.UpgradedIsCompletelyMetrizableSpaceproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- IsClosed.isClopenableproof · cited by 1
- IsOpen.analyticSet_imageproof · cited by 1