reserve A, B, X, Y for set;
reserve R, S, T for non empty TopSpace;

theorem Th41:
  for f being continuous Function of T, S, g being continuous
  Function of T, R holds <:f,g:> is continuous Function of T, [:S,R:]
proof
  let f be continuous Function of T, S, g be continuous Function of T, R;
A1: <:f,g:> = [:f,g:]*(delta the carrier of T) by FUNCT_3:78;
  delta the carrier of T is continuous Function of T,[:T,T:] by Th38;
  hence thesis by A1;
end;
