Theorems · Theorem · general topology
induced_topology_le_preorder
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : TopologicalSpace β] [OrderTopology β]
{f : α → β}, (∀ {x y : α}, f x < f y ↔ x < y) → TopologicalSpace.induced f inst_2 ≤ Preorder.topology α- Defined in
- Mathlib.Topology.Order.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Preorderstatement and proof · cited by 7,952
- Set.ofPredproof · cited by 6,101
- iInfproof · cited by 1,690
- OrderTopologystatement and proof · cited by 1,355
- Filter.principalproof · cited by 740
- Filter.comapproof · cited by 546
- iInf_congr_Propproof · cited by 218
- TopologicalSpace.inducedstatement · cited by 148
- le_iInf₂proof · cited by 67
- inf_le_infproof · cited by 54
- Filter.comap_principalproof · cited by 47
Cited by1
Results whose statement or proof uses this declaration.
- induced_topology_eq_preorderproof · cited by 2