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 ∈ 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 ∈ K whenever X ⊂ Y . These results are applied to investigating properties of absolute retracts for K.

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