Theorems · Definition · algebraic topology

Bundle.Trivialization.piecewise

{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 e' : Bundle.Trivialization F proj) →
                (s : Set B) →
                  e.baseSet ∩ frontier s = e'.baseSet ∩ frontier s →
                    Set.EqOn (↑e) (↑e') (proj ⁻¹' (e.baseSet ∩ frontier s)) → Bundle.Trivialization F proj

Given two bundle trivializations e, e' of proj : Z → B and a set s : Set B such that the base sets of e and e' intersect frontier s on the same set and e p = e' p whenever proj p ∈ e.baseSet ∩ frontier s, e.piecewise e' s Hs Heq is the bundle trivialization over Set.ite s e.baseSet e'.baseSet that is equal to e on proj ⁻¹ s and is equal to e' otherwise.

Defined in

Mathlib.Topology.FiberBundle.Trivialization

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace