continuous_restrictScalars — Mathlib

English

Again, under coherence conditions, the space of continuous linear maps is complete.

Русский

Опять же, при условии когерентности пространство непрерывных линейных отображений полно.

LaTeX

$$$IsCoherentWith\\{s : Set E | IsVonNBounded 𝕜_1 s\\} \\Rightarrow CompleteSpace(E →SL[σ] F)$$$

Lean4

@[continuity, fun_prop]
theorem continuous_restrictScalars : Continuous (restrictScalars 𝕜' : (E →L[𝕜] F) → (E →L[𝕜'] F)) :=
  (isEmbedding_restrictScalars _).continuous

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