toStrongDual — Mathlib

English

The map x' ↦ toWeakDual x' is continuous when viewed as a map from StrongDual to WeakDual.

Русский

Отображение x' ↦ toWeakDual x' непрерывно как отображение StrongDual → WeakDual.

LaTeX

$$$\\text{toWeakDual}:\\ StrongDual\\toWeakDual \\text{ is continuous}$$$

Lean4

/-- For vector spaces `E`, there is a canonical map `WeakDual 𝕜 E → StrongDual 𝕜 E` (the "identity"
mapping). It is a linear equivalence. Here it is implemented as the inverse of the linear
equivalence `StrongDual.toWeakDual` in the other direction. -/
def toStrongDual : WeakDual 𝕜 E ≃ₗ[𝕜] StrongDual 𝕜 E :=
  StrongDual.toWeakDual.symm

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