Gate Continua, Absolute Terminal Continua and Absolute Retracts
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.
J. J. Charatonik et al., "Gate Continua, Absolute Terminal Continua and Absolute Retracts," Houston Journal of Mathematics, University of Houston, Jan 2002.
Mathematics and Statistics
Keywords and Phrases
absolute retract; arc component; arc-like; atriodic; continuum; decomposable; gate; hereditarily unicoherent; n-od; retraction; tree-like
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