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Uspekhi Mat. Nauk, 2007, Volume 62, Issue 2(374), Pages 109–164 (Mi umn6212)  

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

Weakly infinite-dimensional spaces

V. V. Fedorchuk

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

Abstract: In this survey article two new classes of spaces are considered: $m$-$C$-spaces and $w$-$m$-$C$-spaces, $m=2,3,…,\infty$. They are intermediate between the class of weakly infinite-dimensional spaces in the Alexandroff sense and the class of $C$-spaces. The classes of $2$-$C$-spaces and $w$-$2$-$C$-spaces coincide with the class of weakly infinite-dimensional spaces, while the compact $\infty$-$C$-spaces are exactly the $C$-compact spaces of Haver. The main results of the theory of weakly infinite-dimensional spaces, including classification via transfinite Lebesgue dimensions and Luzin–Sierpińsky indices, extend to these new classes of spaces. Weak $m$-$C$-spaces are characterised by means of essential maps to Henderson's $m$-compacta. The existence of hereditarily $m$-strongly infinite-dimensional spaces is proved.

DOI: https://doi.org/10.4213/rm6212

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English version:
Russian Mathematical Surveys, 2007, 62:2, 323–374

Bibliographic databases:

UDC: 515.12
MSC: 54F45
Received: 25.08.2006

Citation: V. V. Fedorchuk, “Weakly infinite-dimensional spaces”, Uspekhi Mat. Nauk, 62:2(374) (2007), 109–164; Russian Math. Surveys, 62:2 (2007), 323–374

Citation in format AMSBIB
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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, “Dimension scales of bicompacta”, Siberian Math. J., 49:3 (2008), 549–561  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    2. Fedorchuk V.V., Osipov E.V., “Certain classes of weakly infinite-dimensional spaces and topological games”, Topology Appl., 156:1 (2008), 61–69  crossref  mathscinet  zmath  isi  elib  scopus
    3. Fedorchuk V.V., “Transfinite dimensions Ind(m)”, Topology Appl., 155:17–18 (2008), 1888–1908  crossref  mathscinet  zmath  isi  elib  scopus
    4. V. V. Fedorchuk, “$C$-spaces and simplicial complexes”, Siberian Math. J., 50:4 (2009), 741–747  mathnet  crossref  mathscinet  isi  elib
    5. Fedorchuk V.V., “$C$-spaces and matrix of infinite-dimensionality”, Topology Appl., 157:17 (2010), 2622–2634  crossref  mathscinet  zmath  isi  elib  scopus
    6. Krupski P., Tuncali M., “Maps of rank $m$”, Houston J. Math., 37:2 (2011), 653–675  mathscinet  zmath  isi  elib
    7. Fedorchuk V.V., “Inductive (M, N)-Dimensions”, Topology Appl., 169:SI (2014), 120–135  crossref  mathscinet  zmath  isi  scopus
  • Успехи математических наук Russian Mathematical Surveys
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