General Relativity says that mass bends space. It provides a parameter called the density parameter to determine how space is bent.

If the density parameter is measured to be greater than 1, then there is enough mass that space curves positively and forms into a closed sphere.

If the density is less than 1 then space is curving negatively and the universe is shaped like a saddle.

If the density is 1 then the universe is flat.

In a spherical universe straight lines are always going to curve along the sphere and you will end up back where you start. If we could look up at the sky we could potentially see the same galaxies from two different sections of the sky because we would be looking at them from the front and back (if the radius of the universe was small enough).

Current measurements to my knowledge suggest the density parameter is 1 and the universe is flat.