Theorems · Theorem · order theory
Topology.IsUpperSet.monotone_to_upperTopology_continuous
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : TopologicalSpace α]
[inst_3 : TopologicalSpace β] [Topology.IsUpperSet α] [Topology.IsUpper β] {f : α → β}, Monotone f → Continuous f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, 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.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Preorderstatement and proof · cited by 7,952
- Continuousstatement · cited by 2,592
- IsOpenproof · cited by 2,400
- Monotonestatement and proof · cited by 1,397
- Topology.IsUpperSetstatement and proof · cited by 32
- Topology.IsUpperstatement and proof · cited by 18
- IsUpperSet.preimageproof · cited by 8
- Topology.IsUpper.isUpperSet_of_isOpenproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsLowerSet.monotone_to_lowerTopology_continuousproof · cited by 0