Theorems · Theorem · general topology

ContinuousAt.comp

∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] {f : X → Y} {x : X} {g : Y → Z},
  ContinuousAt g (f x) → ContinuousAt f x → ContinuousAt (g ∘ f) x

Defined in

Mathlib.Topology.Continuous

Cited by

56 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace