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Mat. Sb., 2004, Volume 195, Number 12, Pages 109–122 (Mi msb868)  

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

An example of a compact Hausdorff space whose Lebesgue, Brouwer, and inductive dimensions are different

V. V. Fedorchuk

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

Abstract: We construct an example of a separable compact Hausdorff space $B$ satisfying the first countability axiom of dimension $2=\dim B<\operatorname{Dg}B=3<\operatorname{ind}B=4=\operatorname{Ind}B$, where $\operatorname{Dg}$ is the inductive dimension invariant introduced by Brouwer in 1913 under the name “Dimensionsgrad”.

DOI: https://doi.org/10.4213/sm868

Full text: PDF file (280 kB)
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English version:
Sbornik: Mathematics, 2004, 195:12, 1809–1822

Bibliographic databases:

UDC: 515.12
MSC: Primary 54F45; Secondary 54D30, 54E45, 54F15
Received: 31.07.2003

Citation: V. V. Fedorchuk, “An example of a compact Hausdorff space whose Lebesgue, Brouwer, and inductive dimensions are different”, Mat. Sb., 195:12 (2004), 109–122; Sb. Math., 195:12 (2004), 1809–1822

Citation in format AMSBIB
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\by V.~V.~Fedorchuk
\paper An example of a~compact Hausdorff space whose Lebesgue, Brouwer, and inductive dimensions are different
\jour Mat. Sb.
\yr 2004
\vol 195
\issue 12
\pages 109--122
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\pages 1809--1822
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  • https://doi.org/10.4213/sm868
  • http://mi.mathnet.ru/eng/msb/v195/i12/p109

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    Citing articles on Google Scholar: Russian citations, English citations
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    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. Charalambous M.G., Krzempek J., “On Dimensionsgrad, resolutions, and chainable continua”, Fundamenta Mathematicae, 209:3 (2010), 243–265  crossref  mathscinet  zmath  isi  elib
    3. Charalambous M.G., Krzempek J., “Rigid continua and transfinite inductive dimension”, Topology and Its Applications, 157:9 (2010), 1690–1702  crossref  mathscinet  zmath  isi
    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
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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