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 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.
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.
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References
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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCMv48n2a07,
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}
}