AANR Spaces and Absolute Retracts for Tree-Like Continua |
| |
| Authors: | Janusz J Charatonik Janusz R Prajs |
| |
| Institution: | (1) Mathematical Institute, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland;(2) Instituto de Matematicas, UNAM, Circuito Exterior, Ciudad Universitaria, 04510 Mexico, D. F., Mexico;(3) Department of Mathematics and Statistics, California State University, Sacramento, CA 95819, USA;(4) Institute of Mathematics, University of Opole, ul. Oleska 48, 45-052 Opole, Poland |
| |
| 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, λ-dendroids, dendroids, arc-like continua and arc-like λ-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. |
| |
| Keywords: | AANR absolute retract arc component arc-like continuum decomposable dendroid hereditarily unicoherent retraction terminal continuum tree-like |
| 本文献已被 SpringerLink 等数据库收录！ |
|
