Theorems · Theorem · general topology
SeparatedNhds.preimage
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {s t : Set Y},
SeparatedNhds s t → Continuous f → SeparatedNhds (f ⁻¹' s) (f ⁻¹' t)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 62 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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.preimagestatement and proof · cited by 4,946
- Continuousstatement and proof · cited by 2,592
- IsOpenproof · cited by 2,400
- Disjointproof · cited by 2,201
- IsOpen.preimageproof · cited by 147
- Set.preimage_monoproof · cited by 95
- SeparatedNhdsstatement and proof · cited by 33
- Disjoint.preimageproof · cited by 22
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsClosedEmbedding.normalSpaceproof · cited by 2