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Inducible mappings between hyperspaces. (English) Zbl 0888.54012

Summary: Given a continuum \(X\) we denote by \(2^X\) and \(C(X)\) the hyperspace of all nonempty compact subsets and of all nonempty subcontinua of \(X\). For any two continua \(X\) and \(Y\) and a mapping \(f:X\to Y\) let \(2^f\) and \(C(f)\) stand for the induced mappings between corresponding hyperspaces. A mapping \(g\) between the hyperspaces is inducible if there exists a mapping \(f\) such that \(g=2^f\) or \(g=C(f)\), respectively. Necessary and sufficient conditions are shown under which a given mapping \(g\) is inducible.

MSC:

54B20 Hyperspaces in general topology
54F15 Continua and generalizations
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