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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.48 no.2 Bogotá July/Dec. 2014 


Transitivity of the Induced Map C_n(f)

Transitividad de la función inducida C_n(f)


1Universidad Industrial de Santander, Bucaramanga, Colombia. Email:
2Universidad Industrial de Santander, Bucaramanga, Colombia. Email:
3Universidad Nacional Autónoma de México, México D. F., México. Email:


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 fk(U)∩ V≠\emptyset. In this paper, we show relationships between transitivity of f and its induced maps Cn(f) and Fn(f), for some n∈N. Also, we present conditions on X such that given a map f:X→ X, the induced function\break Cn(f):Cn(X)→ Cn(X) is not transitive, for any n∈N.

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

2000 Mathematics Subject Classification: 54B20, 37B45, 54F50.


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 Cn(f) y Fn(f), para alguna n∈N. Además, presentamos condiciones sobre X para que dada una función f:X→ X, la función inducida Cn(f):Cn(X)→ Cn(X) no sea transitiva, para ninguna n∈N.

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

Texto completo disponible en PDF


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(Recibido en marzo de 2014. Aceptado en agosto de 2014)

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

    AUTHOR  = {Camargo, Javier and García, Cristian and Ramírez, Ártico},
    TITLE   = {{Transitivity of the Induced Map \boldsymbol{C_n(f)}}},
    JOURNAL = {Revista Colombiana de Matemáticas},
    YEAR    = {2014},
    volume  = {48},
    number  = {2},
    pages   = {235--245}