reserve FT for non empty RelStr;
reserve A for Subset of FT;

theorem
  A` is closed implies A is open
proof
  assume A` is closed;
  then
A1: (A`) = (A`)^b;
  (A`)^b = (((A`)`)^i)` by FIN_TOPO:16
    .= (A^i)`;
  then A = (A^i)`` by A1
    .= A^i;
  hence thesis;
end;
