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import topology.metric_space.isometry
open set
open metric_space
lemma intersection_closed {α : Type*} [metric_space α] {s : ℕ → set α} (h : ∀ n, is_closed (s n)) :
is_closed (⋂ n, s n) :=
begin
exact is_closed_Inter (λ n, h n),
end
