A generalizations of the ternary Cantor set





Cantor set, ternary Cantor set, beta-expantion


In this work, we show a generalization to the ternary Cantor set based on the beta-expantion of a number, futhermore, we present that, under appropriate hypotheses, this extension also corresponds to a constructive way of the definition of the ternary Cantor set . Finally, we prove that these sets that are, in effect, Cantor sets.

Author Biographies

Andres Merino Toapanta, Escuela de Ciencias Físicas y Matemática, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Católica del Ecuador, Quito, Ecuador.

Profesor titular, Escuela de Ciencias Físicas y Matemática

Sebastián Heredia Freire, Departamento de Matemática, Facultad de Ciencias, Escuela Politécnica Nacional, Quito, Ecuador.

Estudiante de la carrera de Matemática, Departamento de Matemática


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How to Cite

Merino Toapanta, A., & Heredia Freire, S. (2020). A generalizations of the ternary Cantor set. Selecciones Matemáticas, 7(02), 222-233. https://doi.org/10.17268/sel.mat.2020.02.04