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No arc-connected treelike continuum is the 2-to-1 image of a continuum.
by
Van Nall
University of Richmond
Coauthors: Jo Heath
In 1940, O. G. Harrold showed that no arc can be the exactly 2-to-1 continuous image of a metric continuum, and in 1947 W. H. Gottschalk showed that no dendrite is a 2-to-1 image. We show that no arc-connected treelike continuum (dendroid) is the 2-to-1 image of a continuum. Thus, an arc connected continuum is the 2-to-1 image of a continuum if and only if it contains two subcontinua whose intersection is not connected.
Date received: January 28, 2003
Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajz-10.