
theorem
  for X be RealUnitarySpace, Y be Subset of X
    holds Y is open iff Y` is closed
proof
  let X be RealUnitarySpace, Y be Subset of X;
  thus Y is open implies Y` is closed;
  assume Y` is closed; then
  consider Z be Subset of RUSp2RNSp X such that
A2: Z = Y` & Z is closed;
  Z` is open by A2;
  hence Y is open by A2;
end;
