Presentation of the theory of normed null bases in a hyperbolic-normal, 4-di-mensional metric space E; i.e. the struc¬ture and properties of all systems of four linearly independent, complex-valued, null vector fields that satisfy the given nor¬malization conditions. It is shown that the system of all normed null bases can be obtained from a given normed null basis by the action of a group of anholonomic matri-ces that are generated from the group of all Jacobian matrices of the Lorentz group under all mappings of the group parameters onto functions of position in E. The an¬holonomic frames, anholonomic connections, and objects of anholonomy arising from normed null bases are studied and a funda¬mental existence theorem is obtained. This existence theorem replaces all equations involving the anholonomic quantities of an unknown normed null basis by equa¬tions involving a known normed null basis and the matrices described above.
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