Theorems · Theorem · general topology

IsCompact.bddBelow_image

∀ {α : Type u_2} {β : Type u_3} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [inst_2 : TopologicalSpace β]
  [ClosedIicTopology α] [Nonempty α] {f : β → α} {K : Set β}, IsCompact K → ContinuousOn f K → BddBelow (f '' K)

A continuous function is bounded below on a compact set.

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

LinearOrderTopologicalSpaceTopologicalSpaceClosedIicTopologyNonempty