IsClosed — Mathlib

English

An unbounded operator is closed exactly when its graph is a closed set.

Русский

Неконечных оператор замкнут тогда, когда его график замкнут как множество.

LaTeX

$$$$ \\text{IsClosed}(f) \\;\\Leftrightarrow\\; (\\mathrm{graph}\, f) \\text{ is closed in } E \\times F $$$$

Lean4

/-- An unbounded operator is closed iff its graph is closed. -/
def IsClosed (f : E →ₗ.[R] F) : Prop :=
  _root_.IsClosed (f.graph : Set (E × F))

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