To the hypothesys of general planes position / S. A. Bogatyi. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2012. № 5. P. 13-19 [Moscow Univ. Math. Bulletin. Vol. 67, N 5, 2012.].
We prove that for some special cases the set of all continuous mappings of an n-dimensional compactum in an m-dimensional Euclidean space such that the set of all d-dimensional planes having the cardinality of the preimage ≥ q has the dimension ≤ qn-(q-d-1)(m-d), is dense.
Key words: dimension, embedding, Euclidean space.