vectorBundle — Mathlib

English

The construction Z yields a full vector bundle over B with total fiber Z.Fiber, whose trivializations are linear and compatible with coordChange.

Русский

Конструкция Z образует полное векторное расслоение над B с общим волокнистым ядром Z.Fiber, тривиализации линейные и согласованы с coordChange.

LaTeX

$$$\text{VectorBundle}(R, F, Z.Fiber)$$$

Lean4

instance vectorBundle : VectorBundle R F Z.Fiber
    where
  trivialization_linear' := by
    rintro _ ⟨i, rfl⟩
    apply localTriv.isLinear
  continuousOn_coordChange' := by
    rintro _ _ ⟨i, rfl⟩ ⟨i', rfl⟩
    refine (Z.continuousOn_coordChange i i').congr fun b hb => ?_
    ext v
    exact Z.localTriv_coordChange_eq i i' hb v

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