If I were you, I would look at the graph of .
I must tell you that I find your questions rather odd.
It is clear that set is clearly not closed (look at the graph).
Therefore it cannot be compact.
It certainly is not open.
As to the idea of bounded, that is not a usual concept considered in topology. But if by bounded you mean that the diameter is finite that clearly it is not bounded.
All of that said, I have no idea what the given, is compact, adds to this question.
I think that you are burden with poor text material.