vectorBundle — Mathlib

English

The memTrivializationAtlas predicate confirms membership for the product continuousLinearMap in the atlas.

Русский

Утверждение memTrivializationAtlas проверяет принадлежность Prod ContinuousLinearMap к атласу.

LaTeX

$$$ \\text{memTrivializationAtlas }(e_1.continuousLinearMap σ e_2) $$$

Lean4

/-- The continuous `σ`-semilinear maps between two vector bundles form a vector bundle. -/
instance vectorBundle : VectorBundle 𝕜₂ (F₁ →SL[σ] F₂) (fun x ↦ E₁ x →SL[σ] E₂ x) :=
  (Bundle.ContinuousLinearMap.vectorPrebundle σ F₁ E₁ F₂ E₂).toVectorBundle

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