Theorems · Theorem · general topology

Monotone.leftOrdContinuous

∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [OrderTopology α]
  [inst_3 : LinearOrder β] {f : α → β} [inst_4 : TopologicalSpace β] [OrderTopology β],
  Monotone f → (∀ (x : α), ContinuousWithinAt f (Set.Iic x) x) → LeftOrdContinuous f

A monotone left-continuous function is left-continuous in the order-theoretic sense.

Defined in

Mathlib.Topology.Order.Monotone

Cited by

1 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderTopologicalSpaceOrderTopologyLinearOrderTopologicalSpaceOrderTopology