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 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;
