1. Let D be the set of finite and infinite sequences over Sigma :=
   {a,b} with c= the prefix ordering.
   a. Verify that this is a domain
   b. Which of the following functions f:D->D is monotone / continuous?
      (i)   f(s) = s with all a's removed
      (ii)  f(s) = abba if s is finite; f(s) = s if s is infinite
      (iii) f(s) = abbas
      (iv)  f(s) = a if s contains finitely many b's; 
            f(s) = b if s contains infinitely many b's
   c. Compute the least fixed point of the f in (b) that are continuous.

2. Let D be a domain with element d and let f be a continuous function
   from D to D. Suppose d <= f(d).
   Is the lub of the chain 
      f^i(d) (i in IN) 
   a fixed point of f? (Check the steps in Tarski's proof to see if it is.)

3. Define the "binary sum of domains" (also called the "disjoint
   union" of domains) that is, given domains D and E, define
   - the set D+E
   - the ordering <= on D+E and prove it is a po
   - a bottom element
   - for (d_i) a chain in D+E the lub of (d_i) and show it is the
     least upperbound
   - injections inl : D -> D+E and inr : E -> D+E that are
     continuous. (You don't have to prove that they are continuous.)