Theorems · Theorem · general topology

Topology.IsEmbedding.continuous_iff

∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} {f : X → Y} {g : Y → Z} [inst : TopologicalSpace X]
  [inst_1 : TopologicalSpace Y] [inst_2 : TopologicalSpace Z],
  Topology.IsEmbedding g → (Continuous f ↔ Continuous (g ∘ f))

Defined in

Mathlib.Topology.Maps.Basic

Cited by

21 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace