Abstract
The concept of topological degree of a map is generalized to the case of discontinuous maps. The numerical value of such a degree may be a rational number. The representations developed are used for topological interpretation of the characteristics of special directions of propagation of acoustic waves in crystals (specifically, acoustic axes). The Euler theorem is generalized to the case of singularities with rational indices, and this result is applied to the set of acoustic axes in crystals.
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