A piece of paper has two sides. However, a Möbius strip has only one side. Ergo, if you walk on a Möbius strip, you walk on both sides and end up on the opposite side on the same location you started at in one trip. Because it has one side, it also has one boundary. This means that if you cut a Möbius strip along its length, you end up with not two rings, but one thinner, longer loop with an extra twist.
A similar structure is the Klein bottle. This structure is a self-paradoxical, single curvature, as its opening meets with its base, making the inside and outside indistinguishable. The entry is the exit, the inside is the outside, and the top is the bottom.
Our universe might be such a space where there is no distinction between the beginning and the end.