I've been trying to figure out a couple of questions, with no luck. Any help would be really appreciated.
1. Let f and g be real valued functions that are uniformly continuous on D. Prove that f + g is uniformly continuous on D.
2. Let f and g be real valued functions that are uniformly continuous on D, and suppose that g(x) does not equal 0 for all x is an element of D.
a. Find an example to show that the function f/g need not be uniformly continuous on D.
b. Prove that if D is compact, then f/g must be uniformly continous on D.
Again, thank you to anyone for any help.