The transitivity of induced maps |
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Authors: | Gerardo Acosta Alejandro Illanes |
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Affiliation: | a Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F., 04510, Mexico b Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F., 04510, Mexico |
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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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Keywords: | primary, 54B20, 37B45 secondary, 54F50, 37B40 |
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