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Transactions of the American Mathematical Society

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



Stability and dimension--a counterexample to a conjecture of Chogoshvili

Author: Yaki Sternfeld
Journal: Trans. Amer. Math. Soc. 340 (1993), 243-251
MSC: Primary 54F45
MathSciNet review: 1145964
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Abstract: 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.

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