toContinuousOrderHom — Mathlib

English

Coercion from F to ContinuousOrderHom α β provides a canonical ContinuousOrderHom structure.

Русский

Ковариация из F в ContinuousOrderHom α β обеспечивает каноническую структуру непрерывного монотонного отображения.

LaTeX

$$def toContinuousOrderHom (f : F) : α →Co β$$

Lean4

/-- Turn an element of a type `F` satisfying `ContinuousOrderHomClass F α β` into an actual
`ContinuousOrderHom`. This is declared as the default coercion from `F` to `α →Co β`. -/
@[coe]
def toContinuousOrderHom (f : F) : α →Co β :=
  { toFun := f
    monotone' := ContinuousOrderHomClass.map_monotone f
    continuous_toFun := map_continuous f }

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