Abstract
We construct a family {Y s: s∈S} of cardinality 2 ℵ 0 of hereditarily indecomposable continua which are: (a) n-dimensional Cantor manifolds, for any given natural number n, or (b) hereditarily strongly infinite-dimensional Cantor manifolds, or else (c) countable-dimensional continua of every given transfinite inductive dimension, small or large, such that if h :Y s→Y s′ is an embedding then s= s′ and h is the identity.
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