Publications de l'Institut Mathématique, Nouvelle SérieVol. 89(103), pp. 49–56 (2011)
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Publications de l'Institut Mathématique, Nouvelle Série Vol. 89(103), pp. 49–56 (2011) |
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HEREDITARILY INDECOMPOSABLE HAUSDORFF CONTINUA HAVE UNIQUE HYPERSPACES $2^X$ AND $C_n(X)$Alejandro IllanesInstituto de Matematicas, Universidad Nacional Autonoma de México, Area de la Investigacion Cientifica, Circuito Exterior, Ciudad Universitaria, México, 04510, D.F., MéxicoAbstract: Let $X$ be a Hausdorff continuum (a compact connected Hausdorff space). Let $2^X$ (respectively, $C_n(X)$) denote the hyperspace of nonempty closed subsets of $X$ (respectively, nonempty closed subsets of $X$ with at most $n$ components), with the Vietoris topology. We prove that if $X$ is hereditarily indecomposable, $Y$ is a Hausdorff continuum and $2^X$ (respectively $C_n(X)$) is homeomorphic to $2^Y$ (respectively, $C_n(Y) $), then $X$ is homeomorphic to $Y$. Keywords: generalized arc, Hausdorff continuum, hereditarily indecomposable, hyperspace, unique hyperspace, Vietoris topology Classification (MSC2000): 54B20 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 6 Apr 2011. This page was last modified: 16 Oct 2012.
© 2011 Mathematical Institute of the Serbian Academy of Science and Arts
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