isClosed_topologicalClosure — Mathlib

English

For non-unital star subalgebras, the topological closure is closed; moreover closures preserve inclusions: closure(s) ≤ t when s ≤ t and t is closed.

Русский

У неполного звёздного подалгебра топологическое closure является замкнутым; closure сохраняет включения: closure(s) ≤ t, если s ≤ t и t замкнуто.

LaTeX

$$$IsClosed\big(s.topologicalClosure\big)$ and $s \le t \implies s.topologicalClosure \le t$ when $t$ is closed$$

Lean4

theorem isClosed_topologicalClosure (s : NonUnitalStarSubalgebra R A) : IsClosed (s.topologicalClosure : Set A) :=
  isClosed_closure

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