isSeqClosed_iff — Mathlib

English

Let s be a subset of a topological space. Then s is sequentially closed if and only if it equals its sequential closure seqClosure(s).

Русский

Пусть s ⊆ X. Тогда s последовательнос zamkнуто, если и только если s равно seqClosure(s).

LaTeX

$$$IsSeqClosed(s) \iff seqClosure(s) = s$$$

Lean4

/-- A set is sequentially closed iff it is equal to its sequential closure. -/
theorem isSeqClosed_iff {s : Set X} : IsSeqClosed s ↔ seqClosure s = s :=
  ⟨IsSeqClosed.seqClosure_eq, isSeqClosed_of_seqClosure_eq⟩

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