Theorems · Theorem · general topology

IsCompact.exists_sInf_image_eq_and_le

∀ {α : Type u_2} {β : Type u_3} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α]
  [inst_2 : TopologicalSpace β] [ClosedIicTopology α] {s : Set β},
  IsCompact s → s.Nonempty → ∀ {f : β → α}, ContinuousOn f s → ∃ x ∈ s, sInf (f '' s) = f x ∧ ∀ y ∈ s, f x ≤ f y

Defined in

Mathlib.Topology.Order.Compact

Cited by

2 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLinearOrderTopologicalSpaceTopologicalSpaceClosedIicTopology