A generalizations of the ternary Cantor set

Authors

DOI:

https://doi.org/10.17268/sel.mat.2020.02.04

Keywords:

Cantor set, ternary Cantor set, beta-expantion

Abstract

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

References

Cantor G. Sur divers théoremes de la théorie des ensembles de points situes dans un espace continua N dimensions. Acta Math Djursholm. 1883; 2:409–414.

Bresoud D. A Radical Approach to Lebesgue’s Theory. New York: Cambridge University Press; 2008.

Dasgupta A. Set Theory with an Introduction to Real Point Sets. New York: Springer; 2013.

Rényi A. Representations for real numbers and their ergodic properties. Acta Math Acad Sci H. 1957; 8(3):477–493.

Cantor G. De la puissance des ensembles parfaits de points. Acta Math Djursholm. 1884; 4(1):381–392.

de Vries M, Komornik V. Unique expansions of real numbers. Adv Math. 2009; 221:390–427.

Vallin R. The Elements of Cantor Sets: With Applications. New Jersey: John Wiley and Sons; 2013.

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Published

2020-12-25

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

Issue

Vol. 7 No. 02 (2020): August - December

Section

Articles

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