Theorems · Theorem · algebraic topology

Bundle.Trivialization.tendsto_nhds_iff

∀ {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] (e : Bundle.Trivialization F proj) {α : Type u_5} {l : Filter α} {f : α → Z} {z : Z},
  z ∈ e.source →
    (Filter.Tendsto f l (nhds z) ↔
      Filter.Tendsto (proj ∘ f) l (nhds (proj z)) ∧ Filter.Tendsto (fun x => (↑e (f x)).2) l (nhds (↑e z).2))

Defined in

Mathlib.Topology.FiberBundle.Trivialization

Cited by

3 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace