Theorems · Theorem · general topology

Topology.IsInducing.continuous_iff

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

Defined in

Mathlib.Topology.Maps.Basic

Cited by

34 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace