Theorems · Theorem · general topology
Topology.IsOpenEmbedding.quasiSeparatedSpace
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β}
[QuasiSeparatedSpace β], Topology.IsOpenEmbedding f → QuasiSeparatedSpace α- Defined in
- Mathlib.Topology.QuasiSeparated
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Set.imageproof · cited by 5,609
- Set.univproof · cited by 3,945
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
- Set.subset_univproof · cited by 228
- QuasiSeparatedSpacestatement and proof · cited by 49
- isQuasiSeparated_univproof · cited by 6
- isQuasiSeparated_univ_iffproof · cited by 4
- IsQuasiSeparated.of_subsetproof · cited by 3
- Topology.IsOpenEmbedding.isQuasiSeparated_iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsOpenEmbedding.spectralSpaceproof · cited by 0