I took it as OP seeking to understand how the topology of space and time are intertwined, and asking whether a spatially closed universe would also be somehow temporally closed.
With this in mind, I felt like establishing the exact relationship between time and space might explain how a spatially closed universe would not necessarily be temporally closed, as the measurement of time involves the measurement of relative distance over multiple frames, which wouldn't necessarily change when measuring at the "boundaries" of a closed spatial loop (since these boundaries are themselves relatively defined)
With this in mind, I felt like establishing the exact relationship between time and space might explain how a spatially closed universe would not necessarily be temporally closed, as the measurement of time involves the measurement of relative distance over multiple frames, which wouldn't necessarily change when measuring at the "boundaries" of a closed spatial loop (since these boundaries are themselves relatively defined)
Apologies to OP if I misunderstood the question.