Consider a universe as a curved 1D line looped onto itself. The second dimension is time. On one hand, this line is easy to visualize as a circle embedded in a flat 2D plane. However, there is only one spatial dimension, so this 2D plane is not real. On the other hand, a 1D space has no intrinsic curvature, but without a curvature, how can this space be looped in a circle? Can anyone please clarify if a 2D universe with the metric signature of (1,1) can be closed and if so how would it be described mathematically?