Theorems · Theorem · general topology

IsCompact.image

∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {s : Set X} {f : X → Y},
  IsCompact s → Continuous f → IsCompact (f '' s)

Defined in

Mathlib.Topology.Compactness.Compact

Cited by

105 results in Mathlib

Foundations

Depth 71 from the axioms, rests on 867 definitions · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace