We investigate absolute retracts for classes of hereditarily unicoherent continua, tree-like continua, λ- dendroids, dendroids and some other related ones. The main results are: (1) the inverse limits of trees with confluent bonding mappings are absolute retracts of hereditarily unicoherent continua; (2) each tree-like continuum is embeddable in a special way in a tree-like absolute retract for the class of hereditarily unicoherent continua; (3) a dendroid is an absolute retract for hereditarily unicoherent continua if and only if it can be embedded as a retract into the Mohler-Nikiel universal smooth dendroid.
J. J. Charatonik et al., "Hereditarily Unicoherent Continua and Their Absolute Retracts," Rocky Mountain Journal of Mathematics, vol. 34, no. 1, pp. 83-110, Arizona State University, Jan 2004.
The definitive version is available at https://doi.org/10.1216/rmjm/1181069893
Mathematics and Statistics
Keywords and Phrases
Absolute retract; arc approximation property; arc property of Kelley; confluent; continuum; decomposable; dendroid
International Standard Serial Number (ISSN)
Article - Journal
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