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Inducible mappings between hyperspaces

Charatonik Janusz J., Charatonik W.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 1

5-9

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 --> Y let 2^f] and C(f) stand for the induced mappings between corresponding hyperspaces. A mapping g between the hypespaces is inducible is 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.