Differential Structure of Space-Time and Physical Fields

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: $\mathrm{\Delta }=2\pi (1-1\mathrm{/}n)$, $n=1,2,\dots$.