We answer a question of Yohe by showing that there exists a family of continuum many topologically different hereditarily indecomposable Cantor manifolds without any non-trivial weakly infinite-dimensional subcon-tinua. This family may consist either of compacta containing one-dimensional subsets or of compacta containing no weakly infinite-dimensional subsets of positive dimension.
Abstract. Any hereditarily indecomposable continuum X of dimension n ≥ 2 is split into layers Br consisting of all points in X that belong to some rdimensional continuum but avoid any non-trivial continuum of dimension less than r. The subjects of this paper are the dimensional and the descriptive properties of the layers Br.
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