2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67364Necessary and/or sufficient conditions are studied for the existence, uniqueness and holonomicity of bases in which on sufficiently general subsets of a differentiable manifold the components of derivations of the tensor algebra over it vanish. The linear connections and the equivalence principle are considered form that point of view.10 LaTeX pages. This paper is a continuation of the e-Prints math.DG/0303373 and math.DG/0304157 and is a preliminary version of the e-Print gr-qc/9805088. For related papers, visit the "publication" pages at http://theo.inrne.bas.bg/~bozho/Differential GeometryGeneral Relativity and Quantum CosmologyMathematical Physics57R25 (Primary) 53B05, 53B99, 53C99, 83C99 (Secondary)Special bases for derivations of tensor algebras. III. Case along smooth maps with separable points of selfintersectiontext