By fixing the distances between all points, the metric also defines the geometry of space-time, and, because there is a meaningful cosmic time, the geometry of space at a given time. Thus space is finite and the universe is said to be closed . The conventional geometry of Euclid. This can be considered as the limit of the other two cases for infinite radius of curvature. Because it is balanced between the other two, this is sometimes called a critical universe.
Space is infinite in all directions.
The universe is infinite in all directions, and so said to be open . At the moment R is increasing with time, which is another way of saying that the Universe is expanding. These possibilities do not affect the solutions for R discussed below, so they get no discussion here. This does not mean the universe seems isotropic to every possible observer.