Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4659747 | Topology and its Applications | 2009 | 21 Pages |
Abstract
For a metric continuum X, we consider the hyperspaces X2 and C(X) of the closed and nonempty subsets of X and of subcontinua of X, respectively, both with the Hausdorff metric. For a given map we investigate the transitivity of the induced maps and . Among other results, we show that if X is a dendrite or a continuum of type λ and is a map, then C(f) is not transitive. However, if X is the Hilbert cube, then there exists a transitive map such that f2 and C(f) are transitive.
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Mathematics
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