isClosedMap_smul_left — Mathlib

English

For a finite basis v, function f, and index i, v.constrL f evaluated at v i equals f i.

Русский

Для конечного базиса v, функции f и индекса i, (v.constrL f)(v_i) = f(i).

LaTeX

$$$v.constrL f (v_i) = f(i)\\quad\\text{for all } i$$$

Lean4

theorem isClosedMap_smul_left [T2Space E] (c : E) : IsClosedMap fun x : 𝕜 => x • c :=
  by
  by_cases hc : c = 0
  · simp_rw [hc, smul_zero]
    exact isClosedMap_const
  · exact (isClosedEmbedding_smul_left hc).isClosedMap

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