Doi: http://dx.doi.org/10.15446/recolma.v48n2.54131

¹Universidad Industrial de Santander, Bucaramanga, Colombia. Email: jcam@matematicas.uis.edu.co
²Universidad Industrial de Santander, Bucaramanga, Colombia. Email: cristianggarcias@hotmail.com
³Universidad Nacional Autónoma de México, México D. F., México. Email: articops@gmail.com

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.

Key words: Transitivity, Induced map, Continua, Hyperspaces of continua, Symmetric products, Continuum of type λ, Dendrites.

Una función continua f: X→ X, definida en un continuo X, se dice transitiva si para cada U y V abiertos diferentes del vacío de X, existe n∈ N, tal que fⁿ(U)∩ V≠\emptyset. En este artículo mostramos relaciones entre la transitividad de f y las funciones inducidas C_n(f) y F_n(f), para alguna n∈N. Además, presentamos condiciones sobre X para que dada una función f:X→ X, la función inducida C_n(f):C_n(X)→ C_n(X) no sea transitiva, para ninguna n∈N.

Palabras clave: Transitividad, función inducida, continuos, hiperespacios de continuos, producto simétrico, continuos tipo λ, dendritas.

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