Geodesic
Generic planes conjecture
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2012), pp. 13-19

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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 $\geq q$ has the dimension $\le qn-(q-d-1)(m-d)$, is dense. 
@article{VMUMM_2012_5_a2,
     author = {S. A. Bogatyi},
     title = {Generic planes conjecture},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {13--19},
     publisher = {mathdoc},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a2/}
}
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S. A. Bogatyi. Generic planes conjecture. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2012), pp. 13-19. http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a2/