Hey sorry for another post. I'm trying to do an assignment and I really don't understand this question

A intersection B is compact. Let B a subset of R2, be as follows: B = { (x,y) in R2s.t. y = sin(1/x), x>0} U {0,0}.

a. Is B closed?, open?, bounded?, compact?

Can you please explain the answer to me, I'm lost. Thanks a lot