Theorems · Theorem · general topology
IsOpen.isClopenable
∀ {α : Type u_1} [inst : TopologicalSpace α] [PolishSpace α] {s : Set α}, IsOpen s → PolishSpace.IsClopenable s- Defined in
- Mathlib.Topology.MetricSpace.Polish
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 166 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
- IsOpenstatement and proof · cited by 2,400
- compl_complproof · cited by 229
- PolishSpacestatement and proof · cited by 57
- IsOpen.isClosed_complproof · cited by 50
- PolishSpace.IsClopenablestatement and proof · cited by 7
- PolishSpace.IsClopenable.complproof · cited by 2
- IsClosed.isClopenableproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- MeasurableSet.isClopenableproof · cited by 5
- PolishSpace.IsClopenable.iUnionproof · cited by 1