reserve r,s,t,u for Real;

theorem Th50:
  for X being LinearTopSpace, V being closed Subset of X, r being
  non zero Real holds r*V is closed
proof
  let X be LinearTopSpace, V be closed Subset of X,
      r be non zero Real;
   reconsider r as non zero Real;
  mlt(r,X).:V = r*V by Th46;
  hence thesis by TOPS_2:58;
end;
