constOfIsEmpty — Mathlib

English

For a fixed index i, the i-th coordinate functional of a ContinuousMultilinearMap yields a ContinuousLinearMap in that coordinate.

Русский

Пусть фиксируем i-ю координату; получаем непрерывный линейный отображение в этой координате.

LaTeX

$$$\\text{toContinuousLinearMap}(f,m,i) : M_i \\to\\! M_2$ with continuity.$$

Lean4

/-- The constant map is multilinear when `ι` is empty. -/
@[simps! toMultilinearMap apply]
def constOfIsEmpty [IsEmpty ι] (m : M₂) : ContinuousMultilinearMap R M₁ M₂
    where
  toMultilinearMap := MultilinearMap.constOfIsEmpty R _ m
  cont := continuous_const

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