Theorems · Theorem · algebraic topology

Bundle.Trivialization.continuousAt_of_comp_left

∀ {B : Type u_1} {F : Type u_2} {Z : Type u_4} [inst : TopologicalSpace B] [inst_1 : TopologicalSpace F] {proj : Z → B}
  [inst_2 : TopologicalSpace Z] {X : Type u_5} [inst_3 : TopologicalSpace X] {f : X → Z} {x : X}
  (e : Bundle.Trivialization F proj),
  ContinuousAt (proj ∘ f) x → proj (f x) ∈ e.baseSet → ContinuousAt (↑e ∘ f) x → ContinuousAt f x

Read off the continuity of a function f : X → Z at x : X by transferring via a trivialization of Z containing f x.

Defined in

Mathlib.Topology.FiberBundle.Trivialization

Cited by

0 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpace