Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, Number 5, Pages 13–19 (Mi vmumm524)  

Mathematics

Generic planes conjecture

S. A. Bogatyi

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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


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English version:
Moscow University Mathematics Bulletin, 2012, 67:5-6, 200–205

Bibliographic databases:

UDC: 515.12
Received: 27.12.2010

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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