Two-to-one maps onto Dendroids
by
Van C. Nall
University of Richmond
Coauthors: Jo Heath (Auburn University)

It is not known whether a tree-like continuum is the image of a 2-to-1 map. In fact, it is not known whether an hereditarly decomposable treelike continuum is the image of a 2-to-1 map. If we assume the continuum is also arc connected (i.e. a dendroid), we can show that it is not the image of a 2-to-1 map from an hereditarily decomposable continuum. It follows that if there is a 2-to-1 map from a continuum onto a dendroid, then there is an at most 2-to-1 map from an indecomposable continuum onto a dendroid. It is not known whether there can be an at most 2-to-1 map from an indecomposable continuum onto a dendroid.

Date received: February 7, 2002