topologicalClosure — Mathlib

English

The topological closure of a nonunital subsemiring is again a nonunital subsemiring.

Русский

Топологическая замкнутость подпол semiring является снова подпол semiring.

LaTeX

$$$(-)_{topologicalClosure}\\colon \\text{NonUnitalSubsemiring}(R) \\to \\text{NonUnitalSubsemiring}(R)$$$

Lean4

/-- The (topological) closure of a non-unital subsemiring of a non-unital topological semiring is
itself a non-unital subsemiring. -/
def topologicalClosure (s : NonUnitalSubsemiring R) : NonUnitalSubsemiring R :=
  { s.toSubsemigroup.topologicalClosure, s.toAddSubmonoid.topologicalClosure with
    carrier := _root_.closure (s : Set R) }

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