Example1.49.Recall from Example 1.36 that given a setXwe defineEXto be theset of partitions onX, and that a partition may be defined using a surjective functions:XPfor some setP.Any surjective functionf:X!Yinduces a monotone mapf:EY! EX, going“backwards”. It is defined by sending a partitions:YPto the compositef:s:XP