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Some thirteen years ago S. B. Nadler, Jr. and L. E. Ward, Jr., asked if any treelike continuum could be the 2-to-1 image of a continuum. In fact, it has been conjectured that the property of being treelike characterizes those continua that are not the 2-to-1 image of any continuum. But the characterization must be something else; this paper shows that many pseudosolenoids are not the 2-to-1 image of any continuum.

A non-treelike continuum that is not the 2-to-1 image of any continuum