Theorems · Theorem · general topology

IsLUB.mem_upperBounds_of_tendsto

∀ {α : Type u_1} {γ : Type u_2} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α]
  [inst_3 : Preorder γ] [inst_4 : TopologicalSpace γ] [OrderClosedTopology γ] {f : α → γ} {s : Set α} {a : α} {b : γ},
  MonotoneOn f s → IsLUB s a → Filter.Tendsto f (nhdsWithin a s) (nhds b) → b ∈ upperBounds (f '' s)

Defined in

Mathlib.Topology.Order.IsLUB

Cited by

3 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderOrderTopologyPreorderTopologicalSpaceOrderClosedTopology