Theorems · Theorem · order theory
GaloisConnection.rightOrdContinuous
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β} {g : β → α},
GaloisConnection f g → RightOrdContinuous gA right adjoint in a Galois connection is right-continuous in the order-theoretic sense.
- Defined in
- Mathlib.Order.OrdContinuous
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.Nonemptyproof · cited by 2,627
- GaloisConnectionstatement and proof · cited by 253
- RightOrdContinuousstatement · cited by 24
- GaloisConnection.isGLB_u_imageproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- OrderIso.rightOrdContinuousproof · cited by 0