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On the Sternfeld-Levin counterexamples to a conjecture of Chogoshvili-Pontrjagin

✍ Scribed by Fredric D. Ancel; Tadeusz Dobrowolski

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
854 KB
Volume
80
Category
Article
ISSN
0166-8641

No coin nor oath required. For personal study only.

✦ Synopsis

An inconclusive proof in a 1937 paper by G. Chogoshvili spawned an interesting dimensiontheoretic conjecture which we call the Chogoshvili-Pontrjagin Conjecture. In 1991, Y. Stemfeld found an ingenious counterexample to this conjecture which he and M. Levin greatly generalized in 1995. In this note we point out a previously unobserved property of the Stemfeld-Levin examples, and we reinterpret their significance in light of this property. Also, we present a version of the Levin-Stemfeld

proof which is more "topological" and less "lattice-theoretic" than the original.

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