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Exactly  -to-1 maps and hereditarily indecomposable tree-like continua |
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| Authors: | Thomas E. Gonzalez |
| Affiliation: | Department of Mathematics, University of West Alabama, Station 7, Livingston, Alabama 35470 |
| Abstract: | In 1947, W.H. Gottschalk proved that no dendrite is the continuous, exactly  -to-1 image of any continuum if  . 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  -to-1 image of any continuum if  . |
| Keywords: | $k$-to-1 map hereditarily indecomposable continua tree-like continua |
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