When do abstract bases generate continuous lattices and L-domains |
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Authors: | Luoshan Xu Xuxin Mao |
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Affiliation: | (1) Department of Mathematics, Yangzhou University, Yangzhou, 225002, P. R. China;(2) College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P. R. China |
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Abstract: | In this note, the new concepts of C-bases (resp., BC-bases, L-bases) which are special kinds of abstract bases are introduced. It is proved that the round ideal completion of a C-basis (resp., BC-basis, L-basis) is a continuous lattice (resp., bc-domain, L-domain). Furthermore, representation theorems of continuous lattices (resp., bc-domains, L-domains) by means of the round ideal completions of C-bases (resp., BC-bases, L-bases) are obtained. Supported by the NSF of China (10371106, 60774073) and by the Fund (S0667-082) from Nanjing University of Aeronautics and Astronautics. |
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Keywords: | 06A11 06B15 06B35 |
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