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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Exactly $k$-to-1 maps and hereditarily indecomposable tree-like continua


Author: Thomas E. Gonzalez
Journal: Proc. Amer. Math. Soc. 131 (2003), 3925-3927
MSC (2000): Primary 54C10
Published electronically: June 30, 2003
MathSciNet review: 1999942
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Abstract: In 1947, W.H. Gottschalk proved that no dendrite is the continuous, exactly $k$-to-1 image of any continuum if $k \geq 2$. Since that time, no other class of continua has been shown to have this same property. It is shown that no hereditarily indecomposable tree-like continuum is the continuous, exactly $k$-to-1 image of any continuum if $k \geq 2$.


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Additional Information

Thomas E. Gonzalez
Affiliation: Department of Mathematics, University of West Alabama, Station 7, Livingston, Alabama 35470
Email: teg@uwa.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06911-9
PII: S 0002-9939(03)06911-9
Keywords: $k$-to-1 map, hereditarily indecomposable continua, tree-like continua
Received by editor(s): March 1, 2001
Received by editor(s) in revised form: June 5, 2001
Published electronically: June 30, 2003
Communicated by: Alan Dow
Article copyright: © Copyright 2003 American Mathematical Society