Covering maps that are not compositions of covering maps of lesser order

摘要

In 1995 J.W. Heath asked which exactly n-to-one maps are compositions of exactly k-to-one maps with 1 < k< n. This paper deals with compositions of covering maps. Exactly n-to-one covering maps on locally arcwise connected continua that are not factorable into covering maps of order greater than or equal to n - 1 are constructed for all n's, and characterized in algebraic terms (fundamental groups). They are not proper compositions of exactly k-to-one maps, open maps, or locally one-to-one maps. [References: 11]