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Mat. Sb. (N.S.), 1988, Volume 135(177), Number 4, Pages 551–557 (Mi msb1724)  

This article is cited in 43 scientific papers (total in 43 papers)

On a problem of P. S. Aleksandrov

A. N. Dranishnikov


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

Full text: PDF file (462 kB)
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English version:
Mathematics of the USSR-Sbornik, 1989, 63:2, 539–545

Bibliographic databases:

UDC: 515.1
MSC: 54F45, 55M10
Received: 24.09.1987

Citation: A. N. Dranishnikov, “On a problem of P. S. Aleksandrov”, Mat. Sb. (N.S.), 135(177):4 (1988), 551–557; 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 Mat. Sb. (N.S.)
\yr 1988
\vol 135(177)
\issue 4
\pages 551--557
\mathnet{http://mi.mathnet.ru/msb1724}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=942139}
\zmath{https://zbmath.org/?q=an:0667.55002|0643.55001}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 63
\issue 2
\pages 539--545
\crossref{https://doi.org/10.1070/SM1989v063n02ABEH003290}


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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. Mardesic S., Rubin L., “Cell-Like Mappings and Nonmetrizable Compacta of Finite Cohomological Dimension”, Trans. Am. Math. Soc., 313:1 (1989), 53–79  crossref  mathscinet  zmath  isi
    2. A. N. Dranishnikov, “Extension of mappings into CW-complexes”, Math. USSR-Sb., 74:1 (1993), 47–56  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. R.J. Daverman, “Hereditarily aspherical compacta and cell-like maps”, Topology and its Applications, 41:3 (1991), 247  crossref  mathscinet  zmath
    4. Dydak J., Walsh J., “Spaces Without Cohomological Dimension Preserving Compactifications”, Proc. Amer. Math. Soc., 113:4 (1991), 1155–1162  crossref  mathscinet  zmath  isi
    5. Dydak J., Kozlowski G., “Vietoris-Begle Theorem and Spectra”, Proc. Amer. Math. Soc., 113:2 (1991), 587–592  crossref  mathscinet  zmath  isi
    6. Dydak J., Walsh J., “Estimates of the Cohomological Dimension of Decomposition Spaces”, Topology Appl., 40:3 (1991), 203–219  crossref  mathscinet  zmath  isi
    7. Rubin L., “Characterizing Cohomological Dimension - the Cohomological Dimension of a-Union-B”, Topology Appl., 40:3 (1991), 233–263  crossref  mathscinet  zmath  isi
    8. Mitchell W., Repovs D., Scepin E., “On 1-Cycles and the Finite Dimensionality of Homology 4-Manifolds”, Topology, 31:3 (1992), 605–623  crossref  mathscinet  zmath  isi
    9. Dranishnikov A., West J., “On Compacta That Intersect Unstably in Euclidean-Space”, Topology Appl., 43:2 (1992), 181–187  crossref  mathscinet  zmath  isi
    10. Dijkstra J., Vanmill J., Mogilski J., “An Ar-Map Whose Range Is More Infinite-Dimensional Than its Domain”, Proc. Amer. Math. Soc., 114:1 (1992), 279–285  crossref  mathscinet  zmath  isi
    11. Dydak J., Walsh J., “Complexes That Arise in Cohomological Dimension Theory - a Unified Approach”, J. Lond. Math. Soc.-Second Ser., 48:2 (1993), 329–347  crossref  mathscinet  zmath  isi
    12. Gladdines H., Vanmill J., “Hyperspaces of Infinite-Dimensional Compacta”, Compos. Math., 88:2 (1993), 143–153  mathscinet  zmath  isi
    13. Dydak J., “Compactifications and Cohomological Dimension”, Topology Appl., 50:1 (1993), 1–10  crossref  mathscinet  zmath  isi
    14. Dydak J., Walsh J., “Infinite Dimensional Compacta Having Cohomological Dimension-2 - an Application of the Sullivan Conjecture”, Topology, 32:1 (1993), 93–104  crossref  mathscinet  zmath  isi
    15. Dobrowolski T., Rubin L., “The Hyperspaces of Infinite-Dimensional Compacta for Covering and Cohomological Dimension Are Homeomorphic”, Pac. J. Math., 164:1 (1994), 15–39  crossref  mathscinet  zmath  isi
    16. Daverman R., Tinsley F., “A Controlled Plus Construction for Crumpled Laminations”, Trans. Am. Math. Soc., 342:2 (1994), 807–826  crossref  mathscinet  zmath  isi
    17. Cauty R., “Linear Metric Space Which Is Not an Absolute Retract”, Fundam. Math., 146:1 (1994), 85–99  crossref  mathscinet  zmath  isi
    18. Watanabe T., “A Note on Cohomological Dimension of Approximate Movable Spaces”, Proc. Amer. Math. Soc., 123:9 (1995), 2883–2885  crossref  mathscinet  zmath  isi
    19. Dydak J., “Realizing Dimension Functions via Homology”, Topology Appl., 65:1 (1995), 1–7  crossref  mathscinet  zmath  isi
    20. Kryszewski W., “Some Homotopy Classification and Extension-Theorems for the Class of Compositions of Acyclic Set-Valued Maps”, Bull. Sci. Math., 119:1 (1995), 21–48  mathscinet  zmath  isi
    21. Moore T., “Gromov-Hausdorff Convergence to Nonmanifolds”, J. Geom. Anal., 5:3 (1995), 411–418  crossref  mathscinet  zmath  isi
    22. Takahisa Miyata, “COHOMOLOGICAL DIMENSION OF UNIFORM SPACES”, Quaestiones Mathematicae, 19:1-2 (1996), 137  crossref  mathscinet  zmath
    23. Alexander N. Dranishnikov, Dušan Repovs, “Cohomological dimension with respect to perfect groups”, Topology and its Applications, 74:1-3 (1996), 123  crossref  mathscinet  zmath
    24. Dijkstra J., “A Dimension Raising Hereditary Shape Equivalence”, Fundam. Math., 149:3 (1996), 265–274  mathscinet  zmath  isi
    25. V. V. Fedorchuk, “The Urysohn identity and dimension of manifolds”, Russian Math. Surveys, 53:5 (1998), 937–974  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    26. Steven C. Ferry, “Limits of polyhedra in Gromov–Hausdorff space”, Topology, 37:6 (1998), 1325  crossref  mathscinet  zmath
    27. Katsuya Yokoi, “Localization in dimension theory”, Topology and its Applications, 84:1-3 (1998), 269  crossref  mathscinet  zmath
    28. Chigogidze A. Zarichnyi M., “On Absolute Extensors Module a Complex”, Topology Appl., 86:2 (1998), 169–178  crossref  mathscinet  zmath  isi
    29. A. V. Karasev, “An infinite-dimensional 4-manifold of finite cohomological dimension with the continuum hypothesis”, Math. Notes, 66:5 (1999), 550–555  mathnet  crossref  crossref  mathscinet  zmath  isi
    30. Dydak J., Mishra S., Shukla R., “On Finitistic Spaces”, Topology Appl., 97:3 (1999), 217–229  crossref  mathscinet  zmath  isi
    31. Semmes S., “Some Topics Concerning Homeomorphic Parameterizations”, Publ. Mat., 45:1 (2001), 3–67  crossref  mathscinet  zmath  isi
    32. V. V. Fedorchuk, “Fully closed mappings and their applications”, J. Math. Sci., 136:5 (2006), 4201–4292  mathnet  crossref  mathscinet  zmath  elib  elib
    33. Chigogidze A. Karasev A., “Topological Model Categories Generated by Finite Complexes”, Mon.heft. Math., 139:2 (2003), 129–150  crossref  mathscinet  zmath  isi
    34. Dranishnikov A., Ferry S., Weinberger S., “Large Riemannian Manifolds Which Are Flexible”, Ann. Math., 157:3 (2003), 919–938  crossref  mathscinet  zmath  isi
    35. Yokoi K., “Bubbly Continua and Homogeneity”, Houst. J. Math., 29:2 (2003), 337–343  mathscinet  zmath  isi
    36. Dydak J., “Extension Theory of Infinite Symmetric Products”, Fundam. Math., 182:1 (2004), 53–77  crossref  mathscinet  zmath  isi
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    38. Dydak J. Levin M., “Extensions of Maps to the Projective Plane”, Algebr. Geom. Topol., 5 (2005), 1711–1718  crossref  mathscinet  zmath  isi
    39. Rubin L., Schapiro P., “Resolutions for Metrizable Compacta in Extension Theory”, Trans. Am. Math. Soc., 358:6 (2006), 2507–2536  crossref  mathscinet  zmath  isi
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    41. Cardenas M., Lasheras F.F., Quintero A., Repovs D., “On Manifolds with Nonhomogeneous Factors”, Cent. Eur. J. Math., 10:3 (2012), 857–862  crossref  mathscinet  zmath  isi
    42. Takahisa Miyata, “A shape theoretic approach to generalized cohomological dimension with respect to topological spaces”, Glas. Mat. Ser. III, 49:1 (2014), 195  crossref  mathscinet  zmath
    43. P. S. Gevorkyan, “Teoriya sheipov”, Fundament. i prikl. matem., 22:6 (2019), 19–84  mathnet
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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