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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.

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On Chogoshvili’s conjecture
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by A. N. Dranishnikov PDF
Proc. Amer. Math. Soc. 125 (1997), 2155-2160 Request permission

Abstract:

There exists a two-dimensional compact subset of $\mathbb {R}^{4}$ having unstable intersection with every affine 2-plane.
References
  • P. Alexandroff, Zum allgemeinen Dimensionsproblem, Gott. Nachrichten 37 (1928).
  • G. Chogoshvili, On a theorem in the theory of dimensionality, Compositio Math. 5 (1938), 292-298.
  • K.A. Sitnikov, An example of a two-dimensional set in three-dimensional Euclidean space which does not separate any regions of that space (in Russian), Dokl. Akad. Nauk SSSR 94 (1954), 1007-1010.
  • G. Nobeling, Die Projektioner einer kompakten m-dimensionalen Menge in $R_{k}$, Ergebnisse Math. Kolloq. 4 (1933), 24-25.
  • S. Mardešić, Compact subsets of $\mathbb {R}^{n}$ and dimension of their projections, Proc. Amer. Math. Soc. 41 (1973), 631-633.
  • M. Levin, A proof of Chogoshvili conjecture for some 2-dimensional compacta, Preprint (1995).
  • D.O. Kiguradze, Some properties of metric dimension (in Russian), Soobsch. Akad. Nauk. Gruz SSR 132:3 (1988), 485-488.
  • Y. Sternfeld, Stability and Dimension - a counterexample to a conjecture of Chogoshvili, Transactions AMS 340 (1) (1993).
  • F. Ancel and T. Dobrowolski, On the Sternfel-Levin Counterexamples to a conjecture of Chogoshvili-Pontryagin, Preprint.
  • A. Dranishnikov, D. Repovs and E. Schepin, On intersection of compacta in euclidean space: the metastable case, Tsukuba J. Math. 17:2 (1993), 549-564.
  • E.M. Chirka, Complex Analytic Sets, Kluwer, Academic Publish, 1989.
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Additional Information
  • A. N. Dranishnikov
  • Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611-8105
  • MR Author ID: 212177
  • Received by editor(s): May 15, 1995
  • Additional Notes: Partially supported by NSF grant DMS-9500875.
  • Communicated by: James E. West
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 2155-2160
  • MSC (1991): Primary 55M10, 54F45
  • DOI: https://doi.org/10.1090/S0002-9939-97-04161-0
  • MathSciNet review: 1425119