On the continuity of limit capacity of central cantor sets

• Muñoz M., Eduardo ^[1] ; Vera V., Jaime ^[1]
  1. [1] Universidad Católica del Norte

     Universidad Católica del Norte

     Antofagasta, Chile

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 11, Nº. 2, 1992, págs. 143-151
• Idioma: inglés
• DOI: 10.22199/S07160917.1992.0002.00006
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• Resumen

  • 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.

• Referencias bibliográficas
  • Citas [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.