Hereditarily indecomposable Hausdorff continua have unique hyperspaces 2X and Cn(X) | Zendy

Alejandro Illanes | Zendy

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Hereditarily indecomposable Hausdorff continua have unique hyperspaces 2X and Cn(X)

Author(s) -

Alejandro Illanes

Publication year - 2011

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1103049i

Subject(s) - hyperspace , indecomposable module , hausdorff space , mathematics , hausdorff distance , urysohn and completely hausdorff spaces , normal space , combinatorics , space (punctuation) , pure mathematics , discrete mathematics , topological space , hausdorff measure , mathematical analysis , hausdorff dimension , computer science , topological vector space , operating system

Communicated by Milos Kurilic Abstract. Let X be a Hausdorff continuum (a compact connected Hausdorff space). Let 2 X (respectively, Cn(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 2X (respectively Cn(X)) is homeomorphic to 2Y (respectively, Cn(Y )), then X is homeomorphic to Y.

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