ИСТИНА

We prove that the homotopy classification of transitive Lie algebroids is reduced to the construction of the final space in the form of the classifying space $BG$, where $G$ is the group ${\bf Aut}(\mathfrak g)^{\delta}$ of automorphisms of the adjoint Lie algebra $\mathfrak g$ with new topology thinner than the classical topology. The description of the classifying space ${\cal B}_{\mathfrak g}$ is reduced to classification of coupling between Lie algebra bundle (LAB) and the tangent bundle. We show that tangent bundle $TM$ can be coupled with the Lie algebra bundle $L$ if and only if the Lie algebra bundle L admits a local trivial structure with structural group endowed with such new topology. More of that we prove that there is a one-to-one correspondence between the family $Coup(L)$ of all coupling of the Lie algebra bundle $L$ with fixed finite dimensional Lie algebra ${\mathfrak g}$ as the fiber and the structural group ${\bf Aut}(\mathfrak g)$ of all automorphisms of Lie algebra $\mathfrak g$ and the tangent bundle $TM$ and the family $LAB^{\delta}(L)$ of equivalent classes of local trivial structures with structural group ${\bf Aut}(\mathfrak g)$ endowed with new topology ${\bf Aut}(\mathfrak g)^{\delta}$.