Theorems · Theorem · general topology

IsClosed.epigraph

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : Preorder α] [t : OrderClosedTopology α]
  [inst_2 : TopologicalSpace β] {f : β → α} {s : Set β},
  IsClosed s → ContinuousOn f s → IsClosed {p | p.1 ∈ s ∧ f p.1 ≤ p.2}

Defined in

Mathlib.Topology.Order.OrderClosed

Cited by

1 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpacePreorderOrderClosedTopologyTopologicalSpace