Theorems · Definition · algebraic topology

Bundle.Trivialization.domExtend

{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] →
              {s : Set B} →
                IsOpen (proj ⁻¹' s) →
                  (Bundle.Trivialization F fun z => proj ↑z) → [Nonempty (Z → F)] → Bundle.Trivialization F proj

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

Defined in

Mathlib.Topology.FiberBundle.Trivialization

Cited by

4 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceNonempty