Theorems · Theorem · general topology

IsCompact.exists_isMinOn_mem_subset

∀ {α : Type u_2} {β : Type u_3} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [inst_2 : TopologicalSpace β]
  [ClosedIicTopology α] {f : β → α} {s t : Set β} {z : β},
  IsCompact t → ContinuousOn f t → z ∈ t → (∀ z' ∈ t \ s, f z < f z') → ∃ x ∈ s, IsMinOn f t x

Defined in

Mathlib.Topology.Order.Compact

Cited by

1 results in Mathlib

Foundations

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

Assumes

LinearOrderTopologicalSpaceTopologicalSpaceClosedIicTopology