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' and characterize spaces which can be mapped onto some universal dendrites under mappings belonging to the considered classes.
J. J. Charatonik et al., "Mapping Hierarchy for Dendrites," Mathematic Dissertation, Institute of Mathematics, Polish Academy of Sciences, Jan 1994.
Mathematics and Statistics
Keywords and Phrases
continuum; confluent; dendrite; monotone mapping; open mapping; light mapping
Article - Journal
© 1994 Institute of Mathematics, Polish Academy of Sciences, All rights reserved.