Gate Continua, Absolute Terminal Continua and Absolute Retracts
Abstract
The following classes K of continua are studied in the paper: (hereditarily decomposable) arc-like, hereditarily irreducible, atriodic, and containing no n-od. If X; Y;Z;K 2 K, with X [ Y = Z, X \ Y = K and X 6= Z 6= Y , then K is called a gate continuum in X for K. We characterize gate subcontinua in members of the above classes K. The characterizations are used to construct absolute terminal continua for K, i.e., continua X in K that are terminal in Y 2 K whenever X º Y . These results are applied to investigating properties of absolute retracts for K.
Recommended Citation
J. J. Charatonik et al., "Gate Continua, Absolute Terminal Continua and Absolute Retracts," Houston Journal of Mathematics, University of Houston, Jan 2002.
Department(s)
Mathematics and Statistics
Keywords and Phrases
absolute retract; arc component; arc-like; atriodic; continuum; decomposable; gate; hereditarily unicoherent; n-od; retraction; tree-like
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2002 University of Houston, All rights reserved.
Publication Date
01 Jan 2002
