A continuum generated by the Sierpiński triangle using inverse limits
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Universidad Industrial de Santander
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Los límites inversos de continuos son una herramienta para cons-truir espacios con propiedades topológicas curiosas a partir de espacios muy simples. A continuación, usaremos los límites inversos y una construcción in-ductiva del triángulo de Sierpiński para construir un continuo que, además de preservar propiedades de autosimilitud, tiene propiedades topológicas interesantes.
Inverse limits are a tool to construct spaces with curious topological properties, from very simple spaces. In this paper, we use inverse limits and an inductive construction of the Sierpinski triangle to build a continuum with very interesting topological properties, in particular, it is self-similar. Keywords: Continua, inverse limit, iterated function system, Sierpiński triangle, atractor, indecomposable continuum, dyadic solenoid, self-similarity, fractals.
Inverse limits are a tool to construct spaces with curious topological properties, from very simple spaces. In this paper, we use inverse limits and an inductive construction of the Sierpinski triangle to build a continuum with very interesting topological properties, in particular, it is self-similar. Keywords: Continua, inverse limit, iterated function system, Sierpiński triangle, atractor, indecomposable continuum, dyadic solenoid, self-similarity, fractals.
Keywords
Continua, inverse limit, iterated function system, Sierpiński triangle, atractor, indecomposable continuum, dyadic solenoid, self-similarity, fractals, Continuos, límite inverso, sistema iterado de funciones, trián-gulo de Sierpiński, atractor, solenoide diádico, au-tosimilitud, fractales