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