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Uspekhi Mat. Nauk, 2002, Volume 57, Issue 2(344), Pages 139–178 (Mi umn498)  

This article is cited in 4 scientific papers (total in 4 papers)

On some problems of topological dimension theory

V. V. Fedorchuk

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

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.

DOI: https://doi.org/10.4213/rm498

Full text: PDF file (466 kB)
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English version:
Russian Mathematical Surveys, 2002, 57:2, 361–398

Bibliographic databases:

UDC: 515.12
MSC: Primary 54F45, 57N13; Secondary 03E30, 54D30, 54D35, 54D20, 54G20, 54E35
Received: 08.10.2001

Citation: V. V. Fedorchuk, “On some problems of topological dimension theory”, Uspekhi Mat. Nauk, 57:2(344) (2002), 139–178; Russian Math. Surveys, 57:2 (2002), 361–398

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. V. V. Fedorchuk, “Fully closed mappings and their applications”, J. Math. Sci., 136:5 (2006), 4201–4292  mathnet  crossref  mathscinet  zmath  elib  elib
    2. Balogh Z., Gruenhage G., “Two more perfectly normal non-metrizable manifolds”, Topology Appl., 151:1-3 (2005), 260–272  crossref  mathscinet  zmath  isi  scopus
    3. V. V. Fedorchuk, “Weakly infinite-dimensional spaces”, Russian Math. Surveys, 62:2 (2007), 323–374  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Krzempek J., “Fully Closed Maps and Non-Metrizable Higher-Dimensional Anderson-Choquet Continua”, Colloquium Mathematicum, 120:2 (2010), 201–222  crossref  mathscinet  zmath  isi
  • Успехи математических наук Russian Mathematical Surveys
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