AANR spaces and absolute retracts for tree-like continua

Charatonik, Janusz Jerzy, and Prajs, Janusz R.. "AANR spaces and absolute retracts for tree-like continua." Czechoslovak Mathematical Journal 55.4 (2005): 877-891. <http://eudml.org/doc/30995>.

@article{Charatonik2005,
abstract = {Continua that are approximative absolute neighborhood retracts (AANR’s) are characterized as absolute terminal retracts, i.e., retracts of continua in which they are embedded as terminal subcontinua. This implies that any AANR continuum has a dense arc component, and that any ANR continuum is an absolute terminal retract. It is proved that each absolute retract for any of the classes of: tree-like continua, $\lambda $-dendroids, dendroids, arc-like continua and arc-like $\lambda $-dendroids is an approximative absolute retract (so it is an AANR). Consequently, all these continua have the fixed point property, which is a new result for absolute retracts for tree-like continua. Related questions are asked.},
author = {Charatonik, Janusz Jerzy, Prajs, Janusz R.},
journal = {Czechoslovak Mathematical Journal},
keywords = {AANR; absolute retract; arc component; arc-like; continuum; decomposable; dendroid; hereditarily unicoherent; retraction; terminal continuum; tree-like; AANR; absolute retract; arc component; arc-like; continuum; decomposable; dendroid},
language = {eng},
number = {4},
pages = {877-891},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {AANR spaces and absolute retracts for tree-like continua},
url = {http://eudml.org/doc/30995},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Charatonik, Janusz Jerzy
AU - Prajs, Janusz R.
TI - AANR spaces and absolute retracts for tree-like continua
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 4
SP - 877
EP - 891
AB - Continua that are approximative absolute neighborhood retracts (AANR’s) are characterized as absolute terminal retracts, i.e., retracts of continua in which they are embedded as terminal subcontinua. This implies that any AANR continuum has a dense arc component, and that any ANR continuum is an absolute terminal retract. It is proved that each absolute retract for any of the classes of: tree-like continua, $\lambda $-dendroids, dendroids, arc-like continua and arc-like $\lambda $-dendroids is an approximative absolute retract (so it is an AANR). Consequently, all these continua have the fixed point property, which is a new result for absolute retracts for tree-like continua. Related questions are asked.
LA - eng
KW - AANR; absolute retract; arc component; arc-like; continuum; decomposable; dendroid; hereditarily unicoherent; retraction; terminal continuum; tree-like; AANR; absolute retract; arc component; arc-like; continuum; decomposable; dendroid
UR - http://eudml.org/doc/30995
ER -