Cosmologist Mark Trodden has an excellent post where he disentangles three questions that most people are interested in knowing about the universe: What is its shape? Is it finite or infinite? Will it expand forever or eventually collapse back into itself?
It is sometimes mistakenly assumed that the three are variations on the same question and that answering one determines the answers to the other two. For example, if the universe if positively curved, then it must imply that it is also finite and will eventually recollapse. Trodden says that this is incorrect and explains what we need to know to answer each one, and concludes:
So the universe may be positively or negatively curved, or flat, and our solutions to GR tell us this. They may be finite or infinite, and connected up in interesting ways, but GR does not tell us why this is the case. And the universe may expand forever or recollapse, but this depends on detailed properties of the cosmic energy budget, and not just on geometry.
Well worth reading.