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Frink quasicontinuous posets

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Abstract

In this paper, the concept of Frink quasicontinuous posets is introduced. The main results are: (1) a poset is a Frink quasicontinuous poset if and only if its normal completion is a quasicontinuous lattice; (2) a poset is precontinuous if and only if it is Frink quasicontinuous and meet precontinuous; (3) when a Frink quasicontinuous poset satisfies certain conditions, the way below relation has the interpolation property; (4) the category of quasicontinuous lattices with complete homomorphisms is a full reflective subcategory of the category of Frink quasicontinuous posets with cut-stable maps.

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Acknowledgments

Supported by the National Natural Science Foundation of China (Nos. 10861007, 11161023), the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 2007B14), the Ganpo 555 programma for leading talents of Jiangxi Province, the NFS of Jiangxi Province (No. 20114BAB201008), the Fund of Education Department of Jiangxi Province (No. GJJ12657).

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Jiangxi Science & Technology Normal University, Nanchang, 330038, China

    Wenfeng Zhang

  2. Department of Mathematics, Jiangxi Normal University, Nanchang, 330022, China

    Xiaoquan Xu

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  1. Wenfeng Zhang
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  2. Xiaoquan Xu
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Correspondence to Wenfeng Zhang.

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Communicated by Michael Mislove.

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Zhang, W., Xu, X. Frink quasicontinuous posets. Semigroup Forum 94, 6–16 (2017). https://doi.org/10.1007/s00233-015-9745-x

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