Theorems · Theorem · general topology

Topology.IsInducing.isLindelof_iff

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

If f : X → Y is an inducing map, the image f '' s of a set s is Lindelöf if and only if s is compact.

Defined in

Mathlib.Topology.Compactness.Lindelof

Cited by

3 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace