Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 30 No. 1 (2012): Revista Integración, temas de matemáticas
Research and Innovation Articles

A continuum generated by the Sierpiński triangle using inverse limits

PDF (Español (España))
  • Javier Camargo,
  • Rafael Isaacs
Javier Camargo
Universidad Industrial de Santander
Rafael Isaacs
Universidad Industrial de Santander

Published 2012-08-21

Keywords

  • Continua,
  • inverse limit,
  • iterated function system,
  • Sierpiński triangle,
  • atractor,
  • indecomposable continuum,
  • dyadic solenoid,
  • self-similarity,
  • fractals
    • ...More
    Less

How to Cite

Camargo, J., & Isaacs, R. (2012). A continuum generated by the Sierpiński triangle using inverse limits. Revista Integración, Temas De matemáticas, 30(1), 1–13. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/2698

Abstract

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.

PDF (Español (España))

Downloads

Download data is not yet available.

References

  1. Arenas G. y Sabogal S.M., Una introducción a la geometría fractal, Ediciones Universidad Industrial de Santander, Bucaramanga, 2011.
  2. Barnsley M., Fractals everywhere, Academic Press, Inc., Boston, MA, 1988.
  3. Charalambous M.G., “The dimension of inverse limits”, Proc. Amer. Math. Soc. 58 (1976), 289–295.
  4. Hutchinson J.E., “Fractals and self-similarity”, Indiana Univ. Math. J. 30 (1981), no. 5, 713–747.
  5. Ingram W.T., “Inverse Limits”, Aportaciones Matemáticas: Investigación 15, Sociedad Matemática Mexicana, México, 2000.
  6. Illanes A. and Nadler S.B., Jr., Hyperspaces. Fundamentals and recent advances, Monographs and Textbooks in Pure and Applied Mathematics, 216. Marcel Dekker, Inc., New York, 1999.
  7. Kuratowski K., Topology, Vol II, Academic Press, New York, 1968.
  8. Macías S., Topics on continua, Chapman & Hall/CRC, Boca Raton, FL, 2005.
  9. Nadler S.B., Jr., Continuum theory. An introduction, Monographs and Textbooks in Pure and Applied Mathematics, 158. Marcel Dekker, Inc., New York, 1992.
  10. Sierpiński W., “Sur une courbe dont tout point est un point de ramification”, Prace Mat.- Fiz 27 (1916), 77-86.
  11. Willard S., General topology, Dover Publication, Inc. Mineola, New York, 2004.