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  • 1 Instituto de Física y Matemáticas, Universidad Tecnológica de la Mixteca, Carretera a Acatlima, Km. 2.5, Huajuapan de León, Oaxaca, C.P. 69000, México
  • | 2 Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, Ciudad de México, CDMX, C.P. 04510, México
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Let X be a topological space. For any positive integer n, we consider the n-fold symmetric product of X, ℱn(X), consisting of all nonempty subsets of X with at most n points; and for a given function ƒ : XX, we consider the induced functions ℱn(ƒ): ℱn(X) → ℱn(X). Let M be one of the following classes of functions: exact, transitive, ℤ-transitive, ℤ+-transitive, mixing, weakly mixing, chaotic, turbulent, strongly transitive, totally transitive, orbit-transitive, strictly orbit-transitive, ω-transitive, minimal, I N, T T++, semi-open and irreducible. In this paper we study the relationship between the following statements: ƒM and ℱn(ƒ) ∈ M.

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