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Regular interval Cantor sets of S 1 and minimality

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Abstract

It is known that not every Cantor set of S 1 is C 1-minimal. In this work we prove that every member of a subfamily of what we here call regular interval Cantor set is not C 1-minimal. We also prove that no member of a class of Cantor sets that includes this subfamily is C 1+∈-minimal, for any ∈ > 0.

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Authors and Affiliations

  1. Instituto de Matemática y Estadística Facultad de Ingeniería CC30, Universidad de la Republica, CP 11300, Montevideo, Uruguay

    Aldo Portela

Authors
  1. Aldo Portela
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Corresponding author

Correspondence to Aldo Portela.

Additional information

Partially supported by CNPq-Brasil and PEDECIBA-Uruguay.

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Cite this article

Portela, A. Regular interval Cantor sets of S 1 and minimality. Bull Braz Math Soc, New Series 40, 53–75 (2009). https://doi.org/10.1007/s00574-009-0002-3

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  • DOI: https://doi.org/10.1007/s00574-009-0002-3

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