Theorems · Theorem · general topology

ContinuousOn.image_uIcc_of_antitoneOn

∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : ConditionallyCompleteLinearOrder α] [OrderTopology α]
  [DenselyOrdered α] {δ : Type u_1} [inst_4 : LinearOrder δ] [inst_5 : TopologicalSpace δ] [OrderClosedTopology δ]
  {a b : α} {f : α → δ},
  ContinuousOn f (Set.uIcc a b) → AntitoneOn f (Set.uIcc a b) → f '' Set.uIcc a b = Set.uIcc (f a) (f b)

Defined in

Mathlib.Topology.Order.IntermediateValue

Cited by

0 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceConditionallyCompleteLinearOrderOrderTopologyDenselyOrderedLinearOrderTopologicalSpaceOrderClosedTopology