http://img14.imageshack.us/img14/6083/72795644.jpg

For the question above, I can only answer part a)

The set is not open or closed since it doesn't contain the neighborhood at 1 and int(S) = {(x,y) in R2 : x^2 + y^2 < 1} \ {(0,0)}. Is it right?

Also, can someone please help me on part b)

Thank you much.