Theorems · Definition · algebraic topology

FiberPrebundle.toFiberBundle

{B : Type u_2} →
  {F : Type u_3} →
    {E : B → Type u_5} →
      [inst : TopologicalSpace B] →
        [inst_1 : TopologicalSpace F] →
          [inst_2 : (x : B) → TopologicalSpace (E x)] → (a : FiberPrebundle F E) → FiberBundle F E

Make a FiberBundle from a FiberPrebundle. Concretely this means that, given a FiberPrebundle structure for a sigma-type E -- which consists of a number of "pretrivializations" identifying parts of E with product spaces U × F -- one establishes that for the topology constructed on the sigma-type using FiberPrebundle.totalSpaceTopology, these "pretrivializations" are actually "trivializations" (i.e., homeomorphisms with respect to the constructed topology).

Defined in

Mathlib.Topology.FiberBundle.Basic

Cited by

1 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace