On the dimensional structure of hereditarily indecomposable continua

Pol, Roman; Reńska, Mirosława

doi:10.1090/S0002-9947-02-02959-8

On the dimensional structure of hereditarily indecomposable continua
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by Roman Pol and Mirosława Reńska

Trans. Amer. Math. Soc. 354 (2002), 2921-2932

DOI: https://doi.org/10.1090/S0002-9947-02-02959-8

Published electronically: March 6, 2002

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Abstract:

Any hereditarily indecomposable continuum $X$ of dimension $n\geq 2$ is split into layers $B_r$ consisting of all points in $X$ that belong to some $r$-dimensional 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 $B_r$.

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