Exactly 𝑘-to-1 maps and hereditarily indecomposable tree-like continua

Abstract

In 1947, W.H. Gottschalk proved that no dendrite is the continuous, exactly k k -to-1 image of any continuum if k ≥ 2 k \geq 2 . 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 k k -to-1 image of any continuum if k ≥ 2 k \geq 2 .