Theorems · Theorem · general topology

IsLindelof.image_of_continuousOn

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

A continuous image of a Lindelöf set is a Lindelöf set.

Defined in

Mathlib.Topology.Compactness.Lindelof

Cited by

1 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace