 reserve X for RealUnitarySpace;
 reserve x, y, y1, y2 for Point of X;

theorem Th22:
  for S be RealUnitarySpace,
      M be non empty Subset of S,
      L be Subset of S
  st L = the carrier of Ort_Comp(M) holds
    L is closed Subset of TopSpaceNorm RUSp2RNSp S
proof
  let S be RealUnitarySpace,
      M be non empty Subset of S,
      L be Subset of S;
  assume L = the carrier of Ort_Comp(M); then
  for seq be sequence of S
    st rng seq c= L & seq is convergent
         holds lim seq in L by Th21;
  hence thesis by Th12;
end;
