Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2012, Number 5, Pages 13–19 (Mi vmumm524)  
Mathematics

Generic planes conjecture

S. A. Bogatyi

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract: 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.
Key words: dimension, embedding, Euclidean space.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1562.2008.1
Russian Foundation for Basic Research 09-01-00741а
Received: 27.12.2010
English version:
Moscow University Mathematics Bulletin, 2012, Volume 67, Issue 5-6, Pages 200–205
DOI: https://doi.org/10.3103/S0027132212050038
Bibliographic databases:
Document Type: Article
UDC: 515.12
Language: Russian
Citation: S. A. Bogatyi, “Generic planes conjecture”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, no. 5, 13–19; Moscow University Mathematics Bulletin, 67:5-6 (2012), 200–205
Citation in format AMSBIB
\Bibitem{Bog12}
\by S.~A.~Bogatyi
\paper Generic planes conjecture
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2012
\issue 5
\pages 13--19
\mathnet{http://mi.mathnet.ru/vmumm524}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2012
\vol 67
\issue 5-6
\pages 200--205
\crossref{https://doi.org/10.3103/S0027132212050038}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84870873457}
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