Hyperspace retractions for curves

Charatonik Janusz J., et al. Hyperspace retractions for curves. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1997. <http://eudml.org/doc/271132>.

@book{CharatonikJanuszJ1997,
abstract = {AbstractWe study retractions from the hyperspace of all nonempty closed subsets of a given continuum onto the continuum (which is naturally embedded in the hyperspace). Some necessary and some sufficient conditions for the existence of such a retraction are found if the continuum is a curve. It is shown that the existence of such a retraction for a curve implies that the curve is a uniformly arcwise connected dendroid, and that a universal smooth dendroid admits such a retraction. The existence of this retraction for a given dendroid implies that the dendroid admits a mean. An example of a (nonplanable) smooth dendroid that admits no mean is constructed. Some related results are obtained and open problems are stated. The results answer several questions asked in the literature.CONTENTS1. Introduction...................................52. Preliminaries.................................73. Hyperspace retractions.................94. Applications to selections............155. Applications to means.................18References.....................................321991 Mathematics Subject Classification: 54B20, 54C15, 54F15, 54F50.},
author = {Charatonik Janusz J., Charatonik Włodzimierz J., Omiljanowski Krzysztof, Prajs Janusz R.},
keywords = {arc-smooth; curve; dendrite; dendroid; hyperspace; inverse limit; mean; retraction; selection; smooth; universal element; smooth dendroid},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Hyperspace retractions for curves},
url = {http://eudml.org/doc/271132},
year = {1997},
}

TY - BOOK
AU - Charatonik Janusz J.
AU - Charatonik Włodzimierz J.
AU - Omiljanowski Krzysztof
AU - Prajs Janusz R.
TI - Hyperspace retractions for curves
PY - 1997
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - AbstractWe study retractions from the hyperspace of all nonempty closed subsets of a given continuum onto the continuum (which is naturally embedded in the hyperspace). Some necessary and some sufficient conditions for the existence of such a retraction are found if the continuum is a curve. It is shown that the existence of such a retraction for a curve implies that the curve is a uniformly arcwise connected dendroid, and that a universal smooth dendroid admits such a retraction. The existence of this retraction for a given dendroid implies that the dendroid admits a mean. An example of a (nonplanable) smooth dendroid that admits no mean is constructed. Some related results are obtained and open problems are stated. The results answer several questions asked in the literature.CONTENTS1. Introduction...................................52. Preliminaries.................................73. Hyperspace retractions.................94. Applications to selections............155. Applications to means.................18References.....................................321991 Mathematics Subject Classification: 54B20, 54C15, 54F15, 54F50.
LA - eng
KW - arc-smooth; curve; dendrite; dendroid; hyperspace; inverse limit; mean; retraction; selection; smooth; universal element; smooth dendroid
UR - http://eudml.org/doc/271132
ER -