MATHEMATICAE

Exactly two-to-one maps from continua onto some tree-like continua by W. D ȩb s k i (Katowice), J. Hea th (Auburn, Ala.) and J. M i odu s z ew sk i (Katowice) Abstract. It is known that no dendrite (Gottschalk 1947) and no hereditarily inde-composable tree-like continuum (J. Heath 1991) can be the image of a continuum under an exactly 2-to-1 (continuous) map. This paper enlarges the class of tree-like continua satisfying this property, namely to include those tree-like continua whose nondegenerate proper subcontinua are arcs. This includes all Knaster continua and Ingram continua. The conjecture that all tree-like continua have this property, stated by S. Nadler Jr. and L. E. Ward Jr. (1983), is still neither confirmed nor rejected. 1. Introduction.