Title

Mapping Hierarchy for Dendrites

Abstract

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.

Department(s)

Mathematics and Statistics

Keywords and Phrases

continuum; confluent; dendrite; monotone mapping; open mapping; light mapping

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1994 Institute of Mathematics, Polish Academy of Sciences, All rights reserved.

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