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 if there exists a surjection f ∈ F of X onto Y. We investigate the quasi-order 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 , and characterize spaces which can be mapped onto some universal dendrites under mappings belonging to the considered classes.
CONTENTS1. Introduction..................................................................52. Preliminaries................................................................63. Hierarchy of spaces.....................................................74. Dendrites.....................................................................95. Monotone and confluent mappings............................136. Open mappings ........................................................227. Problems ...................................................................51References....................................................................51
1991 Mathematics Subject Classification: 54C10, 54F50.
@book{bwmeta1.element.zamlynska-eea5baf4-e92e-463d-a429-a0f6796efcba,
author = {J. J. Charatonik and W. J. Charatonik and J. R. Prajs},
title = {Mapping hierarchy for dendrites},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1994},
zbl = {0822.54009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-eea5baf4-e92e-463d-a429-a0f6796efcba}
}
J. J. Charatonik; W. J. Charatonik; J. R. Prajs. Mapping hierarchy for dendrites. GDML_Books (1994), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-eea5baf4-e92e-463d-a429-a0f6796efcba/