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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2012, Number 5, Pages 13–19
(Mi vmumm524)
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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.
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
Linking options:
https://www.mathnet.ru/eng/vmumm524 https://www.mathnet.ru/eng/vmumm/y2012/i5/p13
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Abstract page: | 176 | Full-text PDF : | 48 | References: | 35 |
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