On the continuity of limit capacity of central cantor sets

Authors

  • Eduardo Muñoz M. Universidad Católica del Norte.
  • Jaime Vera V. Universidad Católica del Norte.

DOI:

https://doi.org/10.22199/S07160917.1992.0002.00006

Keywords:

Topología métrica, Cantor centrales, Hausdorff, Límites

Abstract

A metric topology is defined on the family of central Cantor sets (not necessarily proportionals). In this topology the Hausdorff dimension as well as the limit capacity depend continuously on the central Cantor set. An example of continuous arcs with CONSTANT limit capacity is given.

Author Biographies

Eduardo Muñoz M., Universidad Católica del Norte.

Departamento de Matemática.

Jaime Vera V., Universidad Católica del Norte.

Departamento de Matemática.

References

[1] Hocking, J. & Young, G.: Topology. Addison- Wesley Series in Mathematics., 1961.

[2] Tricot, C.: Two definitions of fractional dimensions. Mathematical Proceedings of the Cambridge Philosophical Society. 91, 1982, pp 57-74.

Published

2018-04-02

How to Cite

[1]
E. Muñoz M. and J. Vera V., “On the continuity of limit capacity of central cantor sets”, Proyecciones (Antofagasta, On line), vol. 11, no. 2, pp. 143-151, Apr. 2018.

Issue

Section

Artículos