Mapping Hierarchy for Dendrites

Let a family S of spaces and a class IF of mappings between members of S be given. For two spaces X and Y in S we define Y SlF X if there exists a surjection f E IF of X onto Y. We investigate the quasi-order SlF in the family of dendrites, where IF is one of the following classes of mappings: retractions, monotone, open, confluent or weakly confluent mappings. In particular, we investigate minimal and maximal elements, chains and antichains in the quasi-order SlF\u27 and characterize spaces which can be mapped onto some universal dendrites under mappings belonging to the considered classes