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Hereditarily Unicoherent Continua and Their Absolute Retracts
- Source :
- Rocky Mountain J. Math. 34, no. 1 (2004), 83-110
- Publication Year :
- 2004
- Publisher :
- Rocky Mountain Mathematics Consortium, 2004.
-
Abstract
- We investigate absolute retracts for classes of hereditarily unicoherent continua, tree-like continua, λdendroids, 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.
- Subjects :
- hereditarily unicoherent
Class (set theory)
Pure mathematics
confluent
General Mathematics
continuum
54C55
unionable
Retract
Dendroid
arc property of Kelley
decomposable
retraction
arc approximation property
Mathematics
Continuum (topology)
Mathematical analysis
arc component
54E40
Absolute retract
tree-like
property of Kelley
54F20
tree
54F15
Tree (set theory)
dendroid
Subjects
Details
- ISSN :
- 00357596
- Volume :
- 34
- Database :
- OpenAIRE
- Journal :
- Rocky Mountain Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....c2b1638af2fd5e823d27917368b7cc33