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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Stability and dimension—a counterexample to a conjecture of Chogoshvili
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by Yaki Sternfeld PDF
Trans. Amer. Math. Soc. 340 (1993), 243-251 Request permission


For every $n \geq 2$ we construct an $n$-dimensional compact subset $X$ of some Euclidean space $E$ so that none of the canonical projections of $E$ on its two-dimensional coordinate subspaces has a stable value when restricted to $X$. This refutes a longstanding claim due to Chogoshvili. To obtain this we study the lattice of upper semicontinuous decompositions of $X$ and in particular its sublattice that consists of monotone decompositions when $X$ is hereditarily indecomposable.
  • R. H. Bing, Higher-dimensional hereditarily indecomposable continua, Trans. Amer. Math. Soc. 71 (1951), 267–273. MR 43452, DOI 10.1090/S0002-9947-1951-0043452-5
  • C. Bessaga and A. Pełczyński, Selected topics in infinite dimensional topology, PWN, Warsaw, 1975.
  • George Chogoshvili, On a theorem in the theory of dimensionality, Compositio Math. 5 (1938), 292–298. MR 1556998
  • R.. Engelking, Math. Rev. 90:k 54047. —, Dimension theory, North-Holland, 1978.
  • Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
  • K. Kuratowski, Topology. II, Academic Press and PWN, 1968. R. Pol, A $2$-dimensional compactum in the product of two $1$-dimensional compacta which does not contain any rectangle, Ulam Quarterly (to appear).
  • K. Sitnikov, Example of a two-dimensional set in three-dimensional Euclidean space allowing arbitrarily small deformations into a one-dimensional polyhedron and a certain new characteristic of the dimension of sets in Euclidean spaces, Doklady Akad. Nauk SSSR (N.S.) 88 (1953), 21–24 (Russian). MR 0054245
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 340 (1993), 243-251
  • MSC: Primary 54F45
  • DOI:
  • MathSciNet review: 1145964