Supposedly, our universe is closed and finite, although the geometry and topology isn't precisely known. This means a straight line (geodesic) traveler must return to his starting poiint, yes/no? Hence, curved space.
At the same time, astronomers claim, that space is flat, to the precision of their measurements. Usually, this is accompanied by the comment that the universe is balanced between infinite expansion, or eventual collapse, we can't tell which.
So, space is closed, but also flat... back in my day, they had something called a logical contradiction, which was considered a bad thing, but I guess times change... viva progress -