Theorems · Theorem · general topology
Topology.IsClosedEmbedding.quasiSober
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β},
Topology.IsClosedEmbedding f → ∀ [QuasiSober β], QuasiSober α- Defined in
- Mathlib.Topology.Sober
- 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.
Cites21
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.imageproof · cited by 5,609
- IsClosedproof · cited by 1,639
- closureproof · cited by 1,254
- Continuous.continuousOnproof · cited by 311
- Topology.IsClosedEmbeddingstatement and proof · cited by 195
- Set.image_singletonproof · cited by 174
- Topology.IsEmbedding.injectiveproof · cited by 103
- IsIrreducibleproof · cited by 59
- QuasiSoberstatement and proof · cited by 31
- Topology.IsClosedEmbedding.toIsEmbeddingproof · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- QuasiSober.of_subsetproof · cited by 1