Theorems · Theorem · general topology
MetricSpace.replaceTopology_eq
∀ {γ : Type u_3} [U : TopologicalSpace γ] (m : MetricSpace γ)
(H : U = PseudoMetricSpace.toUniformSpace.toTopologicalSpace), m.replaceTopology H = m- Defined in
- Mathlib.Topology.MetricSpace.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- MetricSpacestatement and proof · cited by 1,684
- Dist.distproof · cited by 1,539
- Dist.extproof · cited by 9
- MetricSpace.extproof · cited by 5
- MetricSpace.replaceTopologystatement · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.complete_completelyMetrizableMetricproof · cited by 0