Exactly $k$-to-1 maps and hereditarily indecomposable tree-like continua
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- by Thomas E. Gonzalez PDF
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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 $k \geq 2$.References
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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
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3925-3927
- MSC (2000): Primary 54C10
- DOI: https://doi.org/10.1090/S0002-9939-03-06911-9
- MathSciNet review: 1999942