Theorems · Theorem · general topology
IsOpenMap.separableSpace_of_injective
∀ {α : Type u} {β : Type u_1} [t : TopologicalSpace α] [inst : TopologicalSpace β] [TopologicalSpace.SeparableSpace β]
{f : α → β}, IsOpenMap f → Function.Injective f → TopologicalSpace.SeparableSpace α- Defined in
- Mathlib.Topology.Bases
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.preimageproof · cited by 4,946
- Set.Countableproof · cited by 545
- Denseproof · cited by 359
- IsOpenMapstatement and proof · cited by 253
- TopologicalSpace.SeparableSpacestatement and proof · cited by 109
- TopologicalSpace.exists_countable_denseproof · cited by 15
- Dense.preimageproof · cited by 8
- Set.Countable.preimageproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsOpenEmbedding.separableSpaceproof · cited by 1