Theorems · Theorem · general topology
Topology.IsOpenEmbedding.separableSpace
∀ {α : Type u} {β : Type u_1} [t : TopologicalSpace α] [inst : TopologicalSpace β] [TopologicalSpace.SeparableSpace β]
{f : α → β}, Topology.IsOpenEmbedding f → TopologicalSpace.SeparableSpace α- Defined in
- Mathlib.Topology.Bases
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
- TopologicalSpace.SeparableSpacestatement and proof · cited by 109
- Topology.IsEmbedding.injectiveproof · cited by 103
- Topology.IsOpenEmbedding.toIsEmbeddingproof · cited by 61
- Topology.IsOpenEmbedding.isOpenMapproof · cited by 50
- IsOpenMap.separableSpace_of_injectiveproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.separableSpace_sum_iffproof · cited by 0