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Quasicontinuity of Posets via Scott Topology and Sobrification

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Abstract

In this paper, posets which may not be dcpos are considered. In terms of the Scott topology on posets, the new concept of quasicontinuous posets is introduced. Some properties and characterizations of quasicontinuous posets are examined. The main results are: (1) a poset is quasicontinuous iff the lattice of all Scott open sets is a hypercontinuous lattice; (2) the directed completions of quasicontinuous posets are quasicontinuous domains; (3) A poset is continuous iff it is quasicontinuous and meet continuous, generalizing the relevant result for dcpos.

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Authors and Affiliations

  1. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing Jiangsu, 210016, People’s Republic of China

    Xuxin Mao

  2. Department of Mathematics, Yangzhou University, Yangzhou Jiangsu, 225002, People’s Republic of China

    Luoshan Xu

Authors
  1. Xuxin Mao
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  2. Luoshan Xu
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Correspondence to Luoshan Xu.

Additional information

Supported by the NSF of China (10371106, 10410638) and by the Fund (S0667-082) from Nanjing University of Aeronautics and Astronautics.

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Mao, X., Xu, L. Quasicontinuity of Posets via Scott Topology and Sobrification. Order 23, 359–369 (2006). https://doi.org/10.1007/s11083-007-9054-4

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  • DOI: https://doi.org/10.1007/s11083-007-9054-4

Key words

Mathematics Subject Classifications (2000)