theorem Th43:
  for G being BinContinuous TopGroup, a being Element of G holds *
  a is Homeomorphism of G
proof
  let G be BinContinuous TopGroup, a be Element of G;
  set f = *a;
  thus dom f = [#]G & rng f = [#]G & f is one-to-one by FUNCT_2:def 1,def 3;
  thus f is continuous;
  f/" = *(a") by Th18;
  hence thesis;
end;
