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Russian Mathematical Surveys, 2002, Volume 57, Issue 2, Pages 361–398
DOI: https://doi.org/10.1070/RM2002v057n02ABEH000498 (Mi rm498) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On some problems of topological dimension theory

V. V. Fedorchuk

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (426 kB) Citations (5) Russian version article
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DOI: https://doi.org/10.1070/RM2002v057n02ABEH000498
Abstract: This survey is devoted to problems in dimension theory related to the works of Smirnov. New results concern the dimensions of subsets of manifolds. Under the continuum hypothesis we construct two infinite-dimensional 4-manifolds. The first is a manifold “without intermediate dimensions”, that is, every closed subset of it is either infinite-dimensional or of dimension at most four. In the second manifold the dimensions of open subsets take infinitely many values.
Received: 08.10.2001
Bibliographic databases:
Document Type: Article
UDC: 515.12
MSC: Primary 54F45, 57N13; Secondary 03E30, 54D30, 54D35, 54D20, 54G20, 54E35
Language: English
Original paper language: Russian
Citation: V. V. Fedorchuk, “On some problems of topological dimension theory”, Russian Math. Surveys, 57:2 (2002), 361–398
Citation in format AMSBIB
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\by V.~V.~Fedorchuk
\paper On some problems of topological dimension theory
\jour Russian Math. Surveys
\yr 2002
\vol 57
\issue 2
\pages 361--398
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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