Alicia, you are asking the wrong question and trying to get the right answer.... :) Space never existed independently, it is always associated with time. So, the term "Space and Time" would be better. The very typical problem is that we think universe is a 2D and it goes on expaning like the circumference of circle. Then the question is asked, what is outside the circumference of that ......... A BIG ????????? So, space must be infinite :) otherwise there is no way out!! let's assume that the universe is surface of the sphere, or cylinder.... as you wish. ( I prefer sphere) if you walk around , you will find that it seems to infinite but the sphere has finite surface area.. it is easy to visualise it, as we live in 3D world. But The universe is not 3D but 4D or may be even higher Dimension.. So, the universe is the surface of that higher dimesional, which itself has more than two dimension. It is difficult to understand but atleast you can try... So, for me space and time is finite... :):) I don't claim that my claim is correct. you are free to critisise and make corrections. :) Till then,