vectorBundle — Mathlib

English

The VectorPrebundle toVectorBundle equivalence establishes that VectorPrebundle is turned into a VectorBundle with the same fiber data and base topology.

Русский

Эквивалентность toVectorBundle устанавливает, что VectorPrebundle превращается в VectorBundle с тем же волоконным набором и базовой топологией.

LaTeX

$$$$ toVectorBundle(a) = VectorBundle R F E $$$$

Lean4

instance vectorBundle : VectorBundle 𝕜 F (Bundle.Trivial B F)
    where
  trivialization_linear' e
    he := by
    rw [eq_trivialization B F e]
    infer_instance
  continuousOn_coordChange' e e' he
    he' := by
    obtain rfl := eq_trivialization B F e
    obtain rfl := eq_trivialization B F e'
    simp only [trivialization.coordChangeL]
    exact continuous_const.continuousOn

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