Theorems · Theorem · general topology

ContinuousWithinAt.closure_le

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : Preorder α] [t : OrderClosedTopology α]
  [inst_2 : TopologicalSpace β] {f g : β → α} {s : Set β} {x : β},
  x ∈ closure s → ContinuousWithinAt f s x → ContinuousWithinAt g s x → (∀ y ∈ s, f y ≤ g y) → f x ≤ g x

Defined in

Mathlib.Topology.Order.OrderClosed

Cited by

5 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpacePreorderOrderClosedTopologyTopologicalSpace