Would a Long Journey Through the Universe Bring Us Back to Our Starting Point?

The notion of curvature in Earth's sense is applicable to its surface. No one is expecting to find oneself at the starting point having dug through the innards of our precious home.

Why would we consider such a premise in the case of the Universe, when we are clearly not aware of any facts proving an existence of its surface? At best we're inside the Universe.

Moreover, how would one define the 'sameness' of the final point? Is it in relation to neighboring objects or to some static reference point? How one could even ascertain the static property of such a point?

> What shape is the Universe? Or, to put it another way, If you get into a starship, set off in one direction, and keep going, will you eventually return to your starting point, as you would if you set off around the Earth? The jury is still out, apparently, pending further and better information about the curvature of space. “It's a fascinating question to explore. Even though all signs seem to point towards ‘probably not’, there are actually two ways that the answer might turn out to be yes, after all”