TY - JOUR

T1 - Atomic maps and the Chogoshvili-Pontrjagin claim

AU - Levin, M.

AU - Sternfeld, Y.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33646876461&partnerID=8YFLogxK

U2 - 10.1090/s0002-9947-98-01995-3

DO - 10.1090/s0002-9947-98-01995-3

M3 - Article

AN - SCOPUS:33646876461

VL - 350

SP - 4623

EP - 4632

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 11

ER -