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Transactions of the American Mathematical Society

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Atomic maps and
the Chogoshvili-Pontrjagin claim


Authors: M. Levin and Y. Sternfeld
Journal: Trans. Amer. Math. Soc. 350 (1998), 4623-4632
MSC (1991): Primary 54F45
DOI: https://doi.org/10.1090/S0002-9947-98-01995-3
MathSciNet review: 1433123
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Abstract: It is proved that all spaces of dimension three or more disobey the Chogoshvili-Pontrjagin claim. This is of particular interest in view of the recent proof (in Certain 2-stable embeddings, by Dobrowolski, Levin, and Rubin, Topology Appl. 80 (1997), 81-90) that two-dimensional ANRs obey the claim.

The construction utilizes the properties of atomic maps which are maps whose fibers ($=$point inverses) are atoms ($=$hereditarily indecomposable continua).

A construction of M. Brown is applied to prove that every finite dimensional compact space admits an atomic map with a one-dimensional range.


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Additional Information

M. Levin
Affiliation: Department of Mathematics, Haifa University, Mount Carmel, Haifa 31905, Israel
Email: levin@mathcs2.haifa.ac.il

Y. Sternfeld
Affiliation: Department of Mathematics, Haifa University, Mount Carmel, Haifa 31905, Israel
Email: yaki@mathcs2.haifa.ac.il

DOI: https://doi.org/10.1090/S0002-9947-98-01995-3
Received by editor(s): January 17, 1996
Received by editor(s) in revised form: December 5, 1996
Article copyright: © Copyright 1998 American Mathematical Society