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On hereditarily indecomposable continua, Henderson compacta and a question of Yohe

Author: Elzbieta Pol
Journal: Proc. Amer. Math. Soc. 130 (2002), 2789-2795
MSC (2000): Primary 54F15, 54F45
Published electronically: February 4, 2002
MathSciNet review: 1900886
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Abstract: 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 subcontinua. This family may consist either of compacta containing one-dimensional subsets or of compacta containing no weakly infinite-dimensional subsets of positive dimension.

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

Keywords: Hereditarily indecomposable continua, Henderson compacta, hereditarily strongly infinite-dimensional, Cantor manifolds
Received by editor(s): August 23, 2000
Received by editor(s) in revised form: April 4, 2001
Published electronically: February 4, 2002
Additional Notes: The author’s research was partially supported by KBN grant 5 P03A 024 20
Communicated by: Alan Dow
Article copyright: © Copyright 2002 American Mathematical Society