Atriodic Absolute Retracts for Hereditarily Unicoherent Continua
Abstract
Let X be an absolute retract for the class of hereditarily unicoherent continua that contains no simple triod. In this paper we prove that (a) X is atriodic, (b) X is either an arc or an indecomposable continuum having only arcs as its proper subcontinua; (c) if X is either tree-like or circle-like, then it is arc-like.
Recommended Citation
W. J. Charatonik et al., "Atriodic Absolute Retracts for Hereditarily Unicoherent Continua," Houston Journal of Mathematics, vol. 30, no. 4, pp. 1069 - 1088, University of Houston - Mathematics, Jan 2004.
Department(s)
Mathematics and Statistics
Sponsor(s)
Norman Hackerman Advanced Research Program
University of Missouri--Rolla
Keywords and Phrases
Absolute retract; arc approximation property; arc component; arc property of Kelley; continuum; dendroid; hereditarily unicoherent; property of Kelley; retraction; simple triod
International Standard Serial Number (ISSN)
0036-2158
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2004 University of Houston - Mathematics, All rights reserved.
Publication Date
01 Jan 2004
