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
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 340 (1993), 243-251
- MSC: Primary 54F45
- DOI: https://doi.org/10.1090/S0002-9947-1993-1145964-7
- MathSciNet review: 1145964