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Mapping hierarchy for dendrites

J. J. Charatonik; W. J. Charatonik; J. R. Prajs — 1994

AbstractLet a family S of spaces and a class F of mappings between members of S be given. For two spaces X and Y in S we define $Y \leq_{F} X$ if there exists a surjection f ∈ F of X onto Y. We investigate the quasi-order $\leq_{F}$ in the family of dendrites, where F 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 $\leq_{F}$ , and characterize spaces which can be...

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