How can general relativity allow a universe to be finite without having an edge?

In the context of general relativity, the concept of a universe that is finite yet lacks an edge is understood through the geometry of curved space-time.1

Rather than viewing space as a flat, Euclidean container, Albert Einstein demonstrated that the mass and energy within the universe warp the structure of space-time itself. A helpful analogy is the surface of a sphere: if you travel in any direction on a sphere, you will never encounter a boundary or an edge, yet the total surface area remains finite.123

By applying the mathematical approach of Bernhard Riemann, general relativity allows for a closed universe where space is curved back upon itself. In this model, the universe is self-contained; just as one can circumnavigate a globe without ever reaching a "final" point, a path through this finite, curved space would eventually return to its starting position without ever crossing a physical boundary.143