A. N. Dranishnikov, “On a problem of P. S. Aleksandrov”, Math. USSR-Sb., 63:2 (1989), 539

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Mathematics of the USSR-Sbornik, 1989, Volume 63, Issue 2, Pages 539–545
DOI: https://doi.org/10.1070/SM1989v063n02ABEH003290 (Mi sm1724)

This article is cited in 55 scientific papers (total in 55 papers)

On a problem of P. S. Aleksandrov

A. N. Dranishnikov

English version PDF (463 kB) Citations (55) Russian version article

References:

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DOI: https://doi.org/10.1070/SM1989v063n02ABEH003290

Abstract: An old problem of P. S. Aleksandrov, known today as the CE-problem, is solved. Using

K

$K$ -theory, an infinite-dimensional compactum with integer cohomological dimension equal to three is constructed. This shows that cell-like maps may raise dimension.
Bibliography: 9 titles.

Received: 24.09.1987

Bibliographic databases:

UDC: 515.1

MSC: 54F45, 55M10

Language: English

Original paper language: Russian

Citation: A. N. Dranishnikov, “On a problem of P. S. Aleksandrov”, Math. USSR-Sb., 63:2 (1989), 539–545

Citation in format AMSBIB

\Bibitem{Dra88}

\by A.~N.~Dranishnikov

\paper On a problem of P.\,S.~Aleksandrov

\jour Math. USSR-Sb.

\yr 1989

\vol 63

\issue 2

\pages 539--545

\mathnet{http://mi.mathnet.ru/eng/sm1724}

\crossref{https://doi.org/10.1070/SM1989v063n02ABEH003290}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=942139}

\zmath{https://zbmath.org/?q=an:0667.55002|0643.55001}

Linking options:

https://www.mathnet.ru/eng/sm1724

https://doi.org/10.1070/SM1989v063n02ABEH003290

https://www.mathnet.ru/eng/sm/v177/i4/p551

This publication is cited in the following 55 articles:

Vesko Valov, “Separation of homogeneous connected locally compact spaces”, Proc. Amer. Math. Soc. Ser. B, 11:4 (2024), 36
Vesko Valov, “Local structure of homogeneous 𝐴𝑁𝑅-spaces”, Trans. Amer. Math. Soc., 2024
P. S. Gevorgyan, “Shape theory”, J. Math. Sci., 259:5 (2021), 583–627
Takahisa Miyata, “A shape theoretic approach to generalized cohomological dimension with respect to topological spaces”, Glas. Mat. Ser. III, 49:1 (2014), 195
Jerzy Dydak, Akira Koyama, Recent Progress in General Topology III, 2014, 359
Katsuro Sakai, Springer Monographs in Mathematics, Geometric Aspects of General Topology, 2013, 421
Cardenas M., Lasheras F.F., Quintero A., Repovs D., “On Manifolds with Nonhomogeneous Factors”, Cent. Eur. J. Math., 10:3 (2012), 857–862
Dydak J. Levin M., “Maps to the Projective Plane”, Algebr. Geom. Topol., 9:1 (2009), 549–568
Alexandre Karasev, Murat Tuncali, Vesko Valov, Open Problems in Topology II, 2007, 697
Rubin L., Schapiro P., “Resolutions for Metrizable Compacta in Extension Theory”, Trans. Am. Math. Soc., 358:6 (2006), 2507–2536
Daverman R., “Fibrator Properties of Manifolds”, Topology Appl., 153:2-3 (2005), 245–260
Dydak J. Levin M., “Extensions of Maps to the Projective Plane”, Algebr. Geom. Topol., 5 (2005), 1711–1718
Dydak J., “Extension Theory of Infinite Symmetric Products”, Fundam. Math., 182:1 (2004), 53–77
V. V. Fedorchuk, “Fully closed mappings and their applications”, J. Math. Sci., 136:5 (2006), 4201–4292
Chigogidze A. Karasev A., “Topological Model Categories Generated by Finite Complexes”, Mon.heft. Math., 139:2 (2003), 129–150
Dranishnikov A., Ferry S., Weinberger S., “Large Riemannian Manifolds Which Are Flexible”, Ann. Math., 157:3 (2003), 919–938
Yokoi K., “Bubbly Continua and Homogeneity”, Houst. J. Math., 29:2 (2003), 337–343
Robert J. Daverman, Encyclopedia of General Topology, 2003, 97
Semmes S., “Some Topics Concerning Homeomorphic Parameterizations”, Publ. Mat., 45:1 (2001), 3–67
A. V. Karasev, “An infinite-dimensional 4-manifold of finite cohomological dimension with the continuum hypothesis”, Math. Notes, 66:5 (1999), 550–555

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	73

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