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Theorems · Definition · order theory

OmegaCompletePartialOrder.ContinuousHom.toMono

{α : Type u_2} →
  {β : Type u_3} → [inst : OmegaCompletePartialOrder α] → [inst_1 : OmegaCompletePartialOrder β] → (α →𝒄 β) →o α →o β

The map from continuous functions to monotone functions is itself a monotone function.

Defined in
Mathlib.Order.OmegaCompletePartialOrder
Cited by
4 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Quot.sound
Assumes
OmegaCompletePartialOrderOmegaCompletePartialOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

OmegaCompletePartialOrder.ContinuousHom.ωSup · cited by 3ContinuousHom.ωSupOmegaCompletePartialOrder.ContinuousHom.ωSup_apply · cited by 1ContinuousHom.ωSup_applyOmegaCompletePartialOrder.ContinuousHom.toMono_coe · cited by 0ContinuousHom.toMono_coeOmegaCompletePartialOrder.ContinuousHom.ωScottContinuous_apply · cited by 0ContinuousHom.ωScottConti…OmegaCompletePartialOrder.ContinuousHom.ωSup_apply_ωSup · cited by 0ContinuousHom.ωSup_apply_…OrderHom · cited by 934OrderHomOmegaCompletePartialOrder · cited by 104OmegaCompletePartialOrderOrderHomClass.toOrderHom · cited by 44OrderHomClass.toOrderHomOmegaCompletePartialOrder.ContinuousHom · cited by 41OmegaCompletePartialOrder…ContinuousHom.toMonoCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.