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Sbornik: Mathematics, 2005, Volume 196, Issue 11, Pages 1585–1603
DOI: https://doi.org/10.1070/SM2005v196n11ABEH003722 (Mi sm1390) 		 
This article is cited in 8 scientific papers (total in 8 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
English version PDF (289 kB) Citations (8)
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DOI: https://doi.org/10.1070/SM2005v196n11ABEH003722
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).
Received: 24.02.2005
Russian version:
Matematicheskii Sbornik, 2005, Volume 196, Number 11, Pages 33–52
DOI: https://doi.org/10.4213/sm1390
Bibliographic databases:
UDC: 515.127.15
MSC: Primary 54F45; Secondary 55M10, 54C65
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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