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Hereditarily indecomposable continua have unique hyperspace \(2^X\). (English) Zbl 0938.54010

Summary: The author proves that if \(X\) is a hereditarily indecomposable continuum and \(Y\) is a continuum such that \(2^X\) (the hypersurface of compact subsets of \(X\)) is homeomorphic to \(2^Y\) then \(X\) is homeomorphic to \(Y\).

MSC:

54B20 Hyperspaces in general topology
54F15 Continua and generalizations
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