Theorems · Definition · algebraic topology

Bundle.Pretrivialization.domExtend

{B : Type u_1} →
  {F : Type u_2} →
    {Z : Type u_4} →
      [inst : TopologicalSpace B] →
        [inst_1 : TopologicalSpace F] →
          {proj : Z → B} →
            {s : Set B} →
              (Bundle.Pretrivialization F fun z => proj ↑z) → [Nonempty (Z → F)] → Bundle.Pretrivialization F proj

Extend the total space of a pretrivialization from the preimage of a set to the whole space.

Defined in

Mathlib.Topology.FiberBundle.Trivialization

Cited by

4 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceNonempty