Imbeddings and universal compacta



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Some imbedding properties, relative to E[raised to n], of indecomposable, unicoherent, and discoherent continua are characterized by considering extensions of Bellamy's idea of pseudocones. Universal Q-like compacta are found for compacta whose components are Q-like compacta by making use of McCord's results in his paper, "Universal Q-like compacta." Also it is shown that there exists a compactum X such that every continuum is homeomorphic to one of the components of X. In addition, a method of imbedding compacta in continua so as to preserve certain properties possessed by the components of the given compacta is introduced. Characterizations of subcontinua of certain curves are also given. For instance, it is proved that if X is a compactum such that each of its components is either degenerate or tree-like (arc-like), then X can be imbedded in a tree-like (arc-like) curve.