reserve n for Nat;

theorem
  for F being SetSequence of the carrier of TOP-REAL 2, A being Subset
  of TOP-REAL 2 st for i being Nat holds F.i = A holds Lim_sup F = Cl A
proof
  let F be SetSequence of the carrier of TOP-REAL 2, A be Subset of TOP-REAL 2;
  assume
A1: for i being Nat holds F.i = A;
  then Lim_inf F = Lim_sup F by Th39;
  hence thesis by A1,Th23;
end;
