**Hesitating between continuing the expansion and the transition to contraction**

The curvature of space of the universe is one of the factors that determine the law of its expansion. Data of observations do not contradict the fact that three-dimensional space has a small positive curvature, i.e. it is spherical, so that in our time the contribution of curvature to the expansion of the universe does not exceed two percents. The sphericity of space would mean actually its finiteness, so that now we would have observed about one-fiftieth of its full size. In the case if the dark energy density rapidly decreases with time, the presence of positive curvature can lead to the fact that the expansion will be changed into contraction. This turn of events is called the closure of the universe, as opposed to the openness of the universe, when more or less rapid expansion will last indefinitely.