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Mat. Sb., 2005, Volume 196, Number 11, Pages 33–52 (Mi msb1390)  

This article is cited in 7 scientific papers (total in 7 papers)

Roberts-type embeddings and conversion of transversal Tverberg's theorem

S. A. Bogatyia, V. M. Valovb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Nipissing University

Abstract: Central in the paper are two results on the existence of “economical” embeddings in a Euclidean space. The first result (Corollary 1.4) states the existence of an embedding with image intersecting the large-dimensional planes in sets of “controllable” dimension. The second result (Corollary 1.6) proves the existence of maps such that each small-dimensional plane contains “controllably” many points of the image.
Well known results of Nöbeling–Pontryagin, Roberts, Hurewicz, Boltyanskii, and Goodsell can be obtained as consequences of these results. Their infinite-dimensional version concerning an embedding in a Hilbert space is also established (Theorem 1.8).

DOI: https://doi.org/10.4213/sm1390

Full text: PDF file (392 kB)
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English version:
Sbornik: Mathematics, 2005, 196:11, 1585–1603

Bibliographic databases:

UDC: 515.127.15
MSC: Primary 54F45; Secondary 55M10, 54C65
Received: 24.02.2005

Citation: S. A. Bogatyi, V. M. Valov, “Roberts-type embeddings and conversion of transversal Tverberg's theorem”, Mat. Sb., 196:11 (2005), 33–52; Sb. Math., 196:11 (2005), 1585–1603

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bogatyi S.A., “Finite-to-one maps”, Topology Appl., 155:17-18 (2008), 1876–1887  crossref  mathscinet  zmath  isi  elib
    2. Frolkina O., “A Cantor set in $\mathbb R^d$ with “large” projections”, Topology Appl., 157:4 (2010), 745–751  crossref  mathscinet  zmath  isi  elib
    3. S. I. Bogataya, S. A. Bogatyi, E. A. Kudryavtseva, “An inverse theorem on ‘economic’ maps”, Sb. Math., 203:4 (2012), 554–568  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. K. I. Oblakov, T. A. Oblakova, “Embeddings of graphs into Euclidean space under which the number of points that belong to a hyperplane is minimal”, Sb. Math., 203:10 (2012), 1518–1533  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Bogatyi S., Valov V., “Special Embeddings of Finite-Dimensional Compacta in Euclidean Spaces”, Topology Appl., 159:9, SI (2012), 2269–2273  crossref  mathscinet  zmath  isi  elib
    6. Bogataya S., Bogatyi S., Valov V., “Embeddings of Finite-Dimensional Compacta in Euclidean Spaces”, Topology Appl., 159:7, SI (2012), 1670–1677  crossref  mathscinet  zmath  isi  elib
    7. S. A. Bogatyi, “Generic planes conjecture”, Moscow University Mathematics Bulletin, 67:5-6 (2012), 200–205  mathnet  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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