Theorems · Theorem · general topology

Topology.IsEmbedding.isCountablyCompact_iff

∀ {E : Type u_2} {F : Type u_3} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace F] {A : Set E} {f : E → F},
  Topology.IsEmbedding f → (IsCountablyCompact A ↔ IsCountablyCompact (f '' A))

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

Defined in

Mathlib.Topology.Compactness.CountablyCompact

Cited by

1 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace