Theorems · Theorem · general topology
Equiv.polishSpace_induced
∀ {α : Type u_1} {β : Type u_2} [t : TopologicalSpace β] [PolishSpace β] (f : α ≃ β), PolishSpace αPulling back a Polish topology under an equiv gives again a Polish topology.
- Defined in
- Mathlib.Topology.MetricSpace.Polish
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 155 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Equivstatement and proof · cited by 8,337
- TopologicalSpace.inducedstatement · cited by 148
- PolishSpacestatement and proof · cited by 57
- Homeomorph.isClosedEmbeddingproof · cited by 37
- Equiv.toHomeomorphOfIsInducingproof · cited by 8
- Topology.IsClosedEmbedding.polishSpaceproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsClosed.isClopenableproof · cited by 1