M365C Recent Homework, Fall '09 (with links to solutions)
Older homework
syllabus

HW#7 (Due Fri. 10/16): Rosenlicht Ch. III #27,28,30,32,35.

HW#8 (Due Fri. 10/23): Rosenlicht Ch. III #37 (Prove (ii) => (iii) and convince yourself the other implications hold.)
#38 (i.e prove the statement for open sets and also for closed sets).
A. Suppose f: E¹ ->  E¹ satisfies the condition at each x₀ obtained from the definition of continuity at x₀ by interchanging the quantifiers:
There is a delta >0 such that for every epsilon >0, |x-x₀| < delta => |f(x)-f(x₀)| < epsilon.
Prove that f is constant.
Rosenlicht Ch. IV #1b (at x=0),d,2,3.

HW#9 (Due Fri. 10/30): Rosenlicht Ch. IV #7 (the given inequalities should be strict since f(a) is not defined), 8,10,14,16.

HW#10 (Due Fri. 11/6): Rosenlicht Ch. IV #19,20 (i.e. a composite of uniformly continuous functions is uniformly continuous), 21,29a,33b,38.

HW#11 (Due Fri. 11/13): Rosenlicht Ch. IV #42,43,44,46, Ch. V #1a,b,2.

HW#12 (Due Fri. 11/20): Rosenlicht Ch. V #6,8,9a ("Right-hand limit" means the limit on the right side of the equation),11,13,14.

There WILL be a class on Wed. 11/25.

HW#13 (Due Mon. 11/30): Rosenlicht Ch. VI #1,2,3,9,11,16.

HW#14 (not collected; solutions posted Fri. 12/4): Rosenlicht Ch. VI #7,12,17 Ch.VII #4,5