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 is an element of K, with X boolean OR Y = Z, X boolean AND Y = K and X not equal Z not equal 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 is an element of K whenever X subset of Y. These results are applied to investigating properties of absolute retracts for K.