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On intersection of compacta in Euclidean space. II


Author: A. N. Dranishnikov
Journal: Proc. Amer. Math. Soc. 113 (1991), 1149-1154
MSC: Primary 54C25; Secondary 55M10
DOI: https://doi.org/10.1090/S0002-9939-1991-1060721-1
MathSciNet review: 1060721
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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose that $ X$ is a compact subset of $ n$-dimensional Euclidean space $ {\mathbb{R}^n}$. If every map $ f:Y \to {\mathbb{R}^n}$ of a compactum $ Y$ can be approximated by a map avoiding $ X$ then dim $ X \times Y < n$.


References [Enhancements On Off] (What's this?)

  • [D1] A. N. Dranishnikov, An intersection of compacta in Euclidean space, Proc. Amer. Math. Soc. (to appear). MR 1042264 (91h:54024)
  • [D2] -, Homological dimension theory, Uspekhi Mat. Nauk 434 (1988), 11-55. (Russian) MR 969565 (90e:55003)
  • [D3] -, Generalized cohomological dimension of compact metric spaces, Tsukuba Math. J. 14 (1990). MR 1085196 (92d:55002)
  • [D4] -, Spanier- Whitehead duality and stability of intersections of compacta, Trudy Mat. Inst. Steklov. (to appear). (Russian)
  • [Ku] K. Kuratowski, Topology, vol. 2, Academic Press, New York and London, 1968.
  • [Kuz] V. I. Kuzminov, Homological dimension theory, Uspekhi Mat. Nauk 235 (1968), 3-49; Russian Math. Surveys 235 (1968), 1-45. (Russian) MR 0240813 (39:2158)
  • [Sp] E. H. Spanier, Function spaces and duality, Ann. of Math. 70 (1959), 338-378. MR 0107862 (21:6584)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1060721-1
Keywords: Compactum, cohomological dimension, Spanier-Whitehead duality, unstable intersection
Article copyright: © Copyright 1991 American Mathematical Society

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