Mapping of euclidean spaces

In the paper a field of two-dimensional planes is examined. This field is invariant associated with a mapping of twodimensional Euclidean spaces of the same dimensions. A splitting of the spaces on mutually orthogonal two-dimensional planes is proofed. The results are applicable with study of geometrical images associated with the mapping of Euclidean spaces of different dimensions as well as with identification of particular classes of mappings of Euclidean spaces and with mapping classification.