Abstract
After briefly presenting basic ideas of the differential space theory, the global description of space-times in terms of this theory is given. The space-times of a straight cosmic string and that of the closed Friedman world model are our standard examples. A space-time with its singular boundary is no longer a differentiable manifold, but it can be organized into a differential space, and the differential structure of space-time can be prolonged to its singular boundary. In general, the procedure is not unique. A simple classification of differential structure prolongations is also presented.
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