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**Summary:**Looking for detail about what the recollapse of a closed universe would entail

As I understand it, in a universe in which the density parameter is greater than 1, a closed universe, everything would eventually recollapse upon itself. My question is: does this recollapse just refer to all the matter falling back together again, or would the geometric confines of the universe itself get closer and closer together and ultimately disappear?

If we imagine the closed universe as a hypersphere with 3d space curving back on itself, I think it's correct to say if you flew a spaceship in a single direction for an immensely long time you would end up back where you started, right? So does that mean that as the universe collapses, the distance it takes to loop back in on your starting location would lessen? And eventually as the collapse of the universe is about to complete, you could see the back of your own head by staring straight ahead?