Mapping hierarchy for dendrites

J. J. Charatonik; W. J. Charatonik; J. R. Prajs

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1994

Abstract

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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 ≤ F X if there exists a surjection f ∈ F of X onto Y. We investigate the quasi-order ≤ 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 ≤ F , 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

How to cite

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J. J. Charatonik, W. J. Charatonik, and J. R. Prajs. Mapping hierarchy for dendrites. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1994. <http://eudml.org/doc/268525>.

@book{J1994,
abstract = {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 $Y ≤_F X$ if there exists a surjection f ∈ F of X onto Y. We investigate the quasi-order $≤_F$ 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 $≤_\{F\}$, 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},
author = {J. J. Charatonik, W. J. Charatonik, J. R. Prajs},
keywords = {continuum; confluent; dendrite; monotone mapping; open mapping; light mapping; confluent mapping; -mapping},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Mapping hierarchy for dendrites},
url = {http://eudml.org/doc/268525},
year = {1994},
}

TY - BOOK
AU - J. J. Charatonik
AU - W. J. Charatonik
AU - J. R. Prajs
TI - Mapping hierarchy for dendrites
PY - 1994
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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 $Y ≤_F X$ if there exists a surjection f ∈ F of X onto Y. We investigate the quasi-order $≤_F$ 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 $≤_{F}$, 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
LA - eng
KW - continuum; confluent; dendrite; monotone mapping; open mapping; light mapping; confluent mapping; -mapping
UR - http://eudml.org/doc/268525
ER -

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