Proceedings of the American Mathematical Society

Author(s): A. N. Dranishnikov
Journal: Proc. Amer. Math. Soc. 125 (1997), 2155-2160.
MSC (1991): Primary 55M10, 54F45
Retrieve article in: PDF
This article is available free of charge

Abstract: There exists a two-dimensional compact subset of $\mathbb {R}^{4}$ having unstable intersection with every affine 2-plane.

1.: P. Alexandroff, Zum allgemeinen Dimensionsproblem, Gott. Nachrichten 37 (1928).
2.: G. Chogoshvili, On a theorem in the theory of dimensionality, Compositio Math. 5 (1938), 292-298.
3.: 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.
4.: G. Nobeling, Die Projektioner einer kompakten m-dimensionalen Menge in $R_{k}$ , Ergebnisse Math. Kolloq. 4 (1933), 24-25.
5.: S. Mardesic, Compact subsets of ${\mathbb R}^{n}$ and dimension of their projections, Proc. Amer. Math. Soc. 41 (1973), 631-633.
6.: M. Levin, A proof of Chogoshvili conjecture for some 2-dimensional compacta, Preprint (1995).
7.: D.O. Kiguradze, Some properties of metric dimension (in Russian), Soobsch. Akad. Nauk. Gruz SSR 132:3 (1988), 485-488.
8.: Y. Sternfeld, Stability and Dimension - a counterexample to a conjecture of Chogoshvili, Transactions AMS 340 (1) (1993).
9.: F. Ancel and T. Dobrowolski, On the Sternfel-Levin Counterexamples to a conjecture of Chogoshvili-Pontryagin, Preprint.
10.: 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.
11.: E.M. Chirka, Complex Analytic Sets, Kluwer, Academic Publish, 1989.

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 55M10, 54F45

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS