Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On intersections of compacta in Euclidean space
HTML articles powered by AMS MathViewer

by A. N. Dranishnikov PDF
Proc. Amer. Math. Soc. 112 (1991), 267-275 Request permission

Abstract:

Let ${\mathbf {X}}$ be a codimension-three tame compactum in Euclidean space ${{\mathbf {E}}^n}$. If $\operatorname {dim} {\mathbf {X}} \times {\mathbf {Y}} < n$, then every map $f:{\mathbf {Y}} \to {{\mathbf {E}}^n}$ can be approximated by map $g$ with ${\mathbf {X}} \cap \operatorname {Im} g = \emptyset$.
References
    P. Alexandroff, Dimensiotheorie ein Beitrag zur Geometrie der abgeschossenen Mengen, Math. Ann. 106 (1932), 161-238.
  • A. N. Dranishnikov, Homological dimension theory, Uspekhi Mat. Nauk 43 (1988), no. 4(262), 11–55, 255 (Russian); English transl., Russian Math. Surveys 43 (1988), no. 4, 11–63. MR 969565, DOI 10.1070/RM1988v043n04ABEH001900
  • —, Spanier-Whitehead duality and stability of intersection of compacta, Trudy of Steklov Inst. (to appear). (Russian)
  • A. N. Dranišnikov and D. Repovš, On unstable intersections of $2$-dimensional compacta in Euclidean $4$-space, Topology Appl. 54 (1993), no. 1-3, 3–11. MR 1255773, DOI 10.1016/0166-8641(93)90047-H
  • A. N. Dranišnikov, D. Repovš, and E. V. Ščepin, On intersections of compacta of complementary dimensions in Euclidean space, Topology Appl. 38 (1991), no. 3, 237–253. MR 1098904, DOI 10.1016/0166-8641(91)90089-5
  • A. N. Dranishnikov and E. V. Shchepin, Stability of the intersections of compact spaces in a Euclidean space, Uspekhi Mat. Nauk 44 (1989), no. 5(269), 159–160 (Russian); English transl., Russian Math. Surveys 44 (1989), no. 5, 194–195. MR 1040277, DOI 10.1070/RM1989v044n05ABEH002207
  • Robert D. Edwards, Demension theory. I, Geometric topology (Proc. Conf., Park City, Utah, 1974) Lecture Notes in Math., Vol. 438, Springer, Berlin, 1975, pp. 195–211. MR 0394678
  • J. Krasinkiewicz, Homotopy separators and mappings into cubes, Fund. Math. 131 (1988), no. 2, 149–154. MR 974664, DOI 10.4064/fm-131-2-149-154
  • Józef Krasinkiewicz and Krzysztof Lorentz, Disjoint membranes in cubes, Bull. Polish Acad. Sci. Math. 36 (1988), no. 7-8, 397–402 (1989) (English, with Russian summary). MR 1101428
  • V. I. Kuz′minov, Homological dimension theory, Uspehi Mat. Nauk 23 (1968), no. 5 (143), 3–49 (Russian). MR 0240813
  • John Milnor, Construction of universal bundles. II, Ann. of Math. (2) 63 (1956), 430–436. MR 77932, DOI 10.2307/1970012
  • Darryl McCullough and Leonard R. Rubin, Intersections of separators and essential submanifolds of $I^{N}$, Fund. Math. 116 (1983), no. 2, 131–142. MR 716227, DOI 10.4064/fm-116-2-131-142
  • M. A. Štan′ko, Imbedding of compacta in euclidean space, Mat. Sb. (N.S.) 83 (125) (1970), 234–255 (Russian). MR 0271923
  • G. S. Skordev, Mappings that raise dimension, Mat. Zametki 7 (1970), 697–705 (Russian). MR 266208
  • Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
  • S. Spież, Imbeddings in ${{\mathbf {R}}^{2m}}$ of $m$-dimensional compacta with $\operatorname {dim} {\text {(}}{\mathbf {X}} \times {\mathbf {X}}) < {\text {2}}m$, Math. Inst. Polish Acad. Sci., preprint, Warsaw, 1988. —, On pairs of compacta with $\operatorname {dim} {\text {(}}{\mathbf {X}} \times {\mathbf {Y}}) < \operatorname {dim} {\mathbf {X}} + \operatorname {dim} {\mathbf {Y}}$, preliminary report, Math. Inst. Polish Acad. Sci., Warsaw, 1989. S. Spież and H. Toruńczyk, Moving compacta in ${R^m}$ apart, preprint, Warsaw, 1989.
  • Dennis Sullivan, Geometric topology. Part I, Massachusetts Institute of Technology, Cambridge, Mass., 1971. Localization, periodicity, and Galois symmetry; Revised version. MR 0494074
  • John J. Walsh, Dimension, cohomological dimension, and cell-like mappings, Shape theory and geometric topology (Dubrovnik, 1981) Lecture Notes in Math., vol. 870, Springer, Berlin-New York, 1981, pp. 105–118. MR 643526
  • A. V. Zarelua, Finite-to-one mappings of topological spaces and of cohomology manifolds, Sibirsk. Mat. Ž. 10 (1969), 64–92 (Russian). MR 0238308
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54C25, 54F45, 55M10
  • Retrieve articles in all journals with MSC: 54C25, 54F45, 55M10
Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 112 (1991), 267-275
  • MSC: Primary 54C25; Secondary 54F45, 55M10
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1042264-4
  • MathSciNet review: 1042264