reserve S, R for 1-sorted,
  X for Subset of R,
  T for TopStruct,
  x for set;
reserve H for non empty multMagma,
  P, Q, P1, Q1 for Subset of H,
  h for Element of H;
reserve G for Group,
  A, B for Subset of G,
  a for Element of G;

theorem Th30:
  for f, g being Homeomorphism of T holds f * g is Homeomorphism of T
proof
  let f, g be Homeomorphism of T;
  T is non empty or T is empty;
  hence f*g is being_homeomorphism by TOPS_2:57;
end;
