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The dual of a generalized completely distributive lattice is a hypercontinuous lattice

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Abstract

In this short note, we prove that a complete lattice is a generalized completely distributive lattice if and only if its order dual is a hypercontinuous lattice.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, Jiangxi, P. R. China

    Jinbo Yang & Xiaoquan Xu

Authors
  1. Jinbo Yang
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  2. Xiaoquan Xu
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Corresponding author

Correspondence to Jinbo Yang.

Additional information

Presented by F. Wehrung.

Supported by the NFS of China (10331010, 10861007), the Fund for the Author of National Excellent Doctoral Dissertation of China (2007B14), the NFS of Jiangxi Province (2009GZS0012, 2007GZS0179), the Fund of Education Department of Jiangxi Province (GJJ08162).

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Yang, J., Xu, X. The dual of a generalized completely distributive lattice is a hypercontinuous lattice. Algebra Univers. 63, 275–281 (2010). https://doi.org/10.1007/s00012-010-0078-z

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  • DOI: https://doi.org/10.1007/s00012-010-0078-z

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