Theorems · Inductive type · general topology
PolishSpace
(α : Type u_3) → [h : TopologicalSpace α] → Prop
A Polish space is a topological space with second countable topology, that can be endowed
with a metric for which it is complete.
To endow a Polish space with a complete metric space structure, do
letI := upgradeIsCompletelyMetrizable α.
- Defined in
- Mathlib.Topology.MetricSpace.Polish
- Cited by
- 57 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by68
Results whose statement or proof uses this declaration.
- PolishSpace.IsClopenableproof · cited by 7
- MeasurableSet.image_of_continuousOn_injOnstatement and proof · cited by 6
- IsClosed.polishSpacestatement and proof · cited by 6
- MeasureTheory.analyticSet_range_of_polishSpacestatement and proof · cited by 6
- upgradeStandardBorelproof · cited by 5
- MeasurableSet.isClopenablestatement and proof · cited by 5
- MeasurableSet.image_of_monotoneOnstatement and proof · cited by 4
- MeasureTheory.analyticSet_iff_exists_polishSpace_rangestatement and proof · cited by 4
- IsOpen.polishSpacestatement and proof · cited by 2
- Topology.IsClosedEmbedding.polishSpacestatement and proof · cited by 2
- PolishSpace.IsClopenable.complproof · cited by 2
- Measurable.exists_continuousstatement and proof · cited by 2