Collections of higher-dimensional hereditarily indecomposable continua, with incomparable Fréchet types
The paper under review is well written. The author constructs very nice families \(\{Y_s\;|\;s\in S\}\), of cardinality \(2^{\aleph_0}\), of hereditarily indecomposable continua which are: (1) \(n\)-dimensional Cantor manifolds, for any positive integer \(n\); (2) hereditarily strongly infinite-dimensional Cantor manifolds; and (3) countable-dimensional continua of any given transfinite dimension, small or large; such that if \(h\colon Y_s\to Y_{s'}\) is an embedding then \(s=s'\) and \(h\) is the identity map. This work continues the study iniciated by Kelley in 1942. He showed: If there is a hereditarily indecomposable continuum of dimension greater than one, then there exists a hereditarliy indecomposable continuum of infinite dimension (see Theorem 8.7 of: \textit{J. L. Kelley} [Trans. Am. Math. Soc., 52, 22--36 (1942; Zbl 0061.40107)]).
Hereditarily strongly infinite-dimensional
scientific article; zbMATH DE number 2136490
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