Abstract

CAMARGO, JAVIER; GARCIA, CRISTIAN  and  RAMIREZ, ÁRTICO. Transitivity of the Induced Map C_n(f). Rev.colomb.mat. [online]. 2014, vol.48, n.2, pp.235-245. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v48n2.54131.

A map f:X→ X, where X is a continuum, is said to be transitive if for each pair U and V of nonempty open subsets of X, there exists k∈N such that f^k(U)∩ V≠\emptyset. In this paper, we show relationships between transitivity of f and its induced maps C_n(f) and F_n(f), for some n∈N. Also, we present conditions on X such that given a map f:X→ X, the induced function\break C_n(f):C_n(X)→ C_n(X) is not transitive, for any n∈N.

Keywords : Transitivity; Induced map; Continua; Hyperspaces of continua; Symmetric products; Continuum of type λ; Dendrites.

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