Mathlib Map

Theorems · Theorem · general topology

TopologicalSpace.IsCompletelyMetrizableSpace.complete

∀ {X : Type u_3} {t : TopologicalSpace X} [self : TopologicalSpace.IsCompletelyMetrizableSpace X],
  ∃ m, PseudoMetricSpace.toUniformSpace.toTopologicalSpace = t ∧ CompleteSpace X
Defined in
Mathlib.Topology.Metrizable.CompletelyMetrizable
Cited by
1 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
TopologicalSpace.IsCompletelyMetrizableSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

TopologicalSpace.completelyMetrizableMetric · cited by 1TopologicalSpace.complete…TopologicalSpace.complete_completelyMetrizableMetric · cited by 0TopologicalSpace.complete…TopologicalSpace · cited by 24529TopologicalSpaceCompleteSpace · cited by 2532CompleteSpaceMetricSpace · cited by 1684MetricSpaceTopologicalSpace.IsCompletelyMetrizableSpace · cited by 7TopologicalSpace.IsComple…IsCompletelyMetrizableSpace.c…CITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.