Monotone and open Whitney maps defined in 2 X

Abstract

Some equivalent conditions on a Whitney map for 2 X to be open (or monotone) are given. It is shown that the existence of a monotone Whitney map for 2 X implies that the space of Whitney levels in 2 X is pathwise connected. Three examples showing that the contractibility of a dendroid X is independent of the existence of open (or monotone) Whitney maps for 2 X are given and some questions concerning this subject are asked.