Israel Journal of Mathematics

, 133:61

Some mapping theorems for extensional dimension



We present some results related to theorems of Pasynkov and Torunczyk on the geometry of maps of finite dimensional compacta.


  1. [1]
    G. E. Bredon,Sheaf Theory, second edition, Graduate Texts in Mathematics, 170, Springer-Verlag, New York, 1997.MATHGoogle Scholar
  2. [2]
    H. Cohen,A cohomological definition of dimension for locally compact Hausdorff spaces, Duke Mathematical Journal21 (1954), 209–224.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    A. N. Dranishnikov,On the mapping intersection problem, Pacific Journal of Mathematics173 (1996), 403–412.MATHMathSciNetGoogle Scholar
  4. [4]
    A. N. Dranishnikov,On the dimension of the product of two compacta and the dimension of their intersection in general position in Euclidean space, Transactions of the American Mathematical Society352 (2000), 5599–5618.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    A. Dranishnikov and J. Dydak,Extension dimension and extension types, Trudy Matematicheskogo Institut imeni V. A. Steklova212 (1996), Otobrazh. i Razmer., 61–94.MathSciNetGoogle Scholar
  6. [6]
    A. Dranishnikov and J. Dydak,Extension theory of separable metrizable spaces with applications to dimension theory, Transactions of the American Mathematical Society353 (2001), 133–156.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    A. N. Dranishnikov and V. V. Uspenskij,Light maps and extensional dimension, Topology and its Applications80 (1997), 91–99.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    A. N. Dranishnikov, D. Repovš and E. V. Ščepin,Transversal intersection formula for compacta, 8th Prague Topological Symposium on General Topology and Its Relations to Modern Analysis and Algebra (1996), Topology and its Applications85 (1998), 93–117.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    J. Dydak,Cohomological dimension and metrizable spaces. II, Transactions of the American Mathematical Society348 (1996), 1647–1661.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    R. Engelking,Theory of dimensions finite and infinite, Sigma Series in Pure Mathematics, 10, Heldermann Verlag, Lemgo, 1995.MATHGoogle Scholar
  11. [11]
    M. Katětov,On the dimension of non-separable spaces. I, (Russian), Čehoslovack. Mat. Ž.2(77), (1952), 333–368 (1953).Google Scholar
  12. [12]
    J. Krasinkiewicz,On approximation of mappings into 1-manifolds, Bulletin of the Polish Academy of Sciences44 (1996), 431–440.MATHMathSciNetGoogle Scholar
  13. [13]
    M. Levin,Bing maps and finite-dimensional maps, Fundamenta Mathematicae151 (1996), 47–52.MATHMathSciNetGoogle Scholar
  14. [14]
    M. Levin,Certain finite-dimensional maps and their application to hyperspaces, Israel Journal of Mathematics105 (1998), 257–262.MATHMathSciNetCrossRefGoogle Scholar
  15. [15]
    M. Levin,On extensional dimension of maps, Topology and its Applications103 (2000), 33–35.MATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    M. Levin,Some examples in cohomological dimension theory, Pacific Journal of Mathematics202 (2002), 371–378.MATHMathSciNetCrossRefGoogle Scholar
  17. [17]
    M. Levin,On extensional dimension of metrizable spaces, preprint.Google Scholar
  18. [18]
    W. Olszewski,Completion theorem for cohomological dimensions, Proceedings of the American Mathematical Society123 (1995), 2261–2264.MATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    B. A. Pasynkov,The dimension and geometry of mappings (Russian), Doklady Akademii Nauk SSSR221 (1975), 543–546.MathSciNetGoogle Scholar
  20. [20]
    B. A. Pasynkov,On the geometry of continuous mappings of finite-dimensional metrizable compacta (Russian), Trudy Matematicheskogo Institut imeni V. A. Steklova212 (1996), Otobrazh. i Razmer., 147–172.MathSciNetGoogle Scholar
  21. [21]
    L. R. Rubin,Characterizing cohomological dimension: the cohomological dimension of A∪B, Topology and its Applications40 (1991), 233–263.MATHCrossRefMathSciNetGoogle Scholar
  22. [22]
    Y. Sternfeld,On finite-dimensional maps and other maps with “small” fibers, Fundamenta Mathematicae147 (1995), 127–133.MATHMathSciNetGoogle Scholar
  23. [23]
    H. Toruńczyk,Finite-to-one restrictions of continuous functions, Fundamenta Mathematicae125 (1985), 237–249.MathSciNetMATHGoogle Scholar

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© Hebrew University 2003

Authors and Affiliations

  1. 1.Department of MathematicsBen Gurion University of the NegevBe’er ShevaIsrael
  2. 2.Department of MathematicsTexas Tech UniversityLubbockUSA

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