Theorems · Inductive type · general topology
TopologicalSpace.IsCompletelyMetrizableSpace
(X : Type u_3) → [t : TopologicalSpace X] → Prop
A topological space is completely metrizable if there exists a metric space structure
compatible with the topology which makes the space complete.
To endow such a space with a compatible distance, use
letI := upgradeIsCompletelyMetrizable X.
- Cited by
- 7 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 by13
Results whose statement or proof uses this declaration.
- TopologicalSpace.upgradeIsCompletelyMetrizablestatement and proof · cited by 7
- MeasureTheory.StronglyMeasurable.exists_eq_measurable_compstatement and proof · cited by 1
- TopologicalSpace.IsCompletelyMetrizableSpace.completestatement and proof · cited by 1
- TopologicalSpace.completelyMetrizableMetricstatement and proof · cited by 1
- Topology.IsClosedEmbedding.IsCompletelyMetrizableSpacestatement and proof · cited by 1
- MeasureTheory.StronglyMeasurable.limUnderstatement and proof · cited by 1
- TopologicalSpace.IsCompletelyMetrizableSpace_of_isCompletelyPseudoMetrizableSpacestatement · cited by 0
- PolishSpace.casesOnstatement and proof · cited by 0
- TopologicalSpace.IsCompletelyMetrizableSpace.casesOnstatement and proof · cited by 0
- PolishSpace.recOnstatement and proof · cited by 0
- TopologicalSpace.complete_completelyMetrizableMetricstatement and proof · cited by 0
- TopologicalSpace.IsCompletelyMetrizableSpace.recOnstatement and proof · cited by 0