Quasicontinuity of Posets via Scott Topology and Sobrification |
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Authors: | Xuxin Mao Luoshan Xu |
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Institution: | (1) College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing Jiangsu, 210016, People’s Republic of China;(2) Department of Mathematics, Yangzhou University, Yangzhou Jiangsu, 225002, People’s Republic of China |
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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.
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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Keywords: | quasicontinuous poset meet continuous poset Scott topology directed completion sobrification |
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