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Mat. Sb., 1991, Volume 182, Number 9, Pages 1300–1310 (Mi msb1367)  

This article is cited in 24 scientific papers (total in 24 papers)

Extension of mappings into CW-complexes

A. N. Dranishnikov

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: It is determined under what conditions the standard problem of extension of a mapping $f\colon A\to M$ to the whole space $X$ is solvable for any closed subset $A\subset X$. For finite-dimensional metric compacta $X$ and CW-complexes $M$ this is equivalent to the system of inequalities $\textrm{c-}{\dim}_{\pi_k(M)}X\leqslant k$. The result is applied to finding conditions for general position of a compactum in a Euclidean space.

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English version:
Mathematics of the USSR-Sbornik, 1993, 74:1, 47–56

Bibliographic databases:

UDC: 515.1
MSC: Primary 55S36; Secondary 54C20, 54F45
Received: 03.12.1990

Citation: A. N. Dranishnikov, “Extension of mappings into CW-complexes”, Mat. Sb., 182:9 (1991), 1300–1310; Math. USSR-Sb., 74:1 (1993), 47–56

Citation in format AMSBIB
\by A.~N.~Dranishnikov
\paper Extension of mappings into CW-complexes
\jour Mat. Sb.
\yr 1991
\vol 182
\issue 9
\pages 1300--1310
\jour Math. USSR-Sb.
\yr 1993
\vol 74
\issue 1
\pages 47--56

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    This publication is cited in the following articles:
    1. A. N. Dranishnikov, “The Eilenberg–Borsuk theorem for mappings into an arbitrary complex”, Russian Acad. Sci. Sb. Math., 81:2 (1995), 467–475  mathnet  crossref  mathscinet  zmath  isi
    2. E. V. Shchepin, “Arithmetic of dimension theory”, Russian Math. Surveys, 53:5 (1998), 975–1069  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. A.N. Dranishnikov, D. Repovš, E.V. Ščepin, “Transversal intersection formula for compacta”, Topology and its Applications, 85:1-3 (1998), 93  crossref  mathscinet  zmath
    4. Katsuya Yokoi, “Localization in dimension theory”, Topology and its Applications, 84:1-3 (1998), 269  crossref  mathscinet  zmath
    5. Alѣksandr Nikolaѣvich Dranishnikov, Aleksandr Nikolaevich Dranishnikov, Alѣksandr Nikolaѣvich Dranishnikov, Aleksandr Nikolaevich Dranishnikov, “O tѣorii prodolzhѣniya otobrazhѣnii kompaktov”, UMN, 53:5 (1998), 65  mathnet  crossref  mathscinet
    6. Chigogidze A. Fedorchuk V., “On Some Dimensional Properties of 4-Manifolds”, Topology Appl., 107:1-2 (2000), 67–78  crossref  mathscinet  zmath  isi
    7. Zarichnyi M., “Extension Property and Anr-Systems”, Topology Appl., 107:1-2 (2000), 207–214  crossref  mathscinet  zmath  isi
    8. Dranishnikov A. Dydak J., “Extension Theory of Separable Metrizable Spaces with Applications to Dimension Theory”, Trans. Am. Math. Soc., 353:1 (2000), 133–156  crossref  mathscinet  isi
    9. A Dranishnikov, “On Alexandroff theorem for general Abelian groups”, Topology and its Applications, 111:3 (2001), 343  crossref  mathscinet  zmath  elib
    10. A.N. Dranishnikov, J.E. Keesling, “The Countable Extension Basis Theorem and its applications”, Topology and its Applications, 113:1-3 (2001), 29  crossref  mathscinet  zmath
    11. V. V. Fedorchuk, “Fully closed mappings and their applications”, J. Math. Sci., 136:5 (2006), 4201–4292  mathnet  crossref  mathscinet  zmath  elib  elib
    12. N Brodsky, A Chigogidze, “Hurewicz theorem for extension dimension”, Topology and its Applications, 129:2 (2003), 145  crossref  mathscinet  zmath
    13. A. Chigogidze, “Extraordinary dimension theories generated by complexes”, Topology and its Applications, 138:1-3 (2004), 1  crossref  mathscinet  zmath
    14. Dydak J., “Extension Theory of Infinite Symmetric Products”, Fundam. Math., 182:1 (2004), 53–77  crossref  mathscinet  zmath  isi
    15. Dydak J., Levin M., “Extensions of Maps to the Projective Plane”, Algebr. Geom. Topol., 5 (2005), 1711–1718  crossref  mathscinet  zmath  isi
    16. Skordev G., Valov V., “Dimension-Raising Theorems for Cohomological and Extension Dimensions”, Topology Appl., 155:17-18 (2008), 2090–2101  crossref  mathscinet  zmath  isi  elib
    17. Dydak J., Levin M., “Maps to the Projective Plane”, Algebr. Geom. Topol., 9:1 (2009), 549–568  crossref  mathscinet  zmath  isi
    18. Fedorchuk V.V., “Several Remarks on Dimensions Modulo Anr-Compacta”, Topology Appl., 157:4, SI (2010), 716–723  crossref  mathscinet  zmath  isi  elib
    19. Fedorchuk V.V., “Inductive Dimensions Modulo Simplicial Complexes and Anr-Compacta”, Colloq. Math., 120:2 (2010), 223–247  crossref  mathscinet  zmath  isi
    20. Takahisa Miyata, “Approximate extension property of mappings”, Topology and its Applications, 2011  crossref  mathscinet
    21. T. Banakh, A. Karassev, R. Cauty, “ON HOMOTOPICAL AND HOMOLOGICAL $Z_N$-SETS”, Topology Proceedings, 38 (2011), 29–82  mathscinet  zmath  elib
    22. Valov V., “Parametric Bing and Krasinkiewicz Maps: Revisited”, Proc. Amer. Math. Soc., 139:2 (2011), 747–756  crossref  mathscinet  zmath  isi  elib
    23. Vera Tonić, “A proof of the Edwards–Walsh resolution theorem without Edwards–Walsh CW-complexes”, Topology and its Applications, 2012  crossref  mathscinet
    24. Banakh T., Valov V., “Dissertationes Mathematicae”, Diss. Math., 2013, no. 491, 1–120  mathscinet  isi
  • Математический сборник - 1991 Sbornik: Mathematics (from 1967)
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