A few extra answers for some of the suggested study problems from Section 3.4.  I'm not 
intending to post a solutions manual for this section, so details are sparse; talk to us via 
email or in person if you're having trouble justifying the correct answer.

1.  The following are true: (a,b,d,f,g,h)

2.  In this problem, (c,d,e,f) are not covered in this course.  Of the remaining parts,
    (a,i) are true.

3.  Answers are in the back.

4.  (a) every point in this set is a boundary point, as is 0.
    (b) {0,5}
    (c) every point in this set is a boundary point, as are 0 and 2
    (d) every point in this set is a boundary point, as is sqrt(2)
    (e) {2}

5.  (a) Neither
    (b) Closed
    (c) Neither.  (every pt is a boundary pt, but so are all the irrationals)
    (d) Both.  (It's the empty set)
    (e) Closed.  It's [4.5,5.5]
    (f) Open.  Its (-infinity,0)U(0,infinity)