  A physical interpretation of axioms of the differential structure of
space-time is presented. Consequences of such interpretation for cosmic
string's space-time with a scalar field are studied. It is shown that the
assumption of smoothness of the scalar field leads either to modification of
cosmic string's space-time global properties or to quantization of the deficit
of angle: $\Delta =2\pi (1-1/n)$, $n=1,2,\dots$.
