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On the dimensional structure of hereditarily indecomposable continua

Authors: Roman Pol and Miroslawa Renska
Journal: Trans. Amer. Math. Soc. 354 (2002), 2921-2932
MSC (1991): Primary 54F15, 54F45, 54H05
Published electronically: March 6, 2002
MathSciNet review: 1895209
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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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Additional Information

Roman Pol
Affiliation: Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland

Miroslawa Renska
Affiliation: Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland

Keywords: Hereditarily indecomposable continua, dimension, Borel sets
Received by editor(s): September 5, 2000
Received by editor(s) in revised form: October 5, 2001
Published electronically: March 6, 2002
Additional Notes: Research partially supported by KBN grant 5 P03A 024 20
Article copyright: © Copyright 2002 American Mathematical Society