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Lim-inf convergence in partially ordered sets |
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| Authors: | Bin Zhao Dongsheng Zhao |
| Affiliation: | a Department of Mathematics, Shaanxi Normal University, Xi'an 710062, PR China b Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, 637616, Singapore |
| Abstract: | The lim-inf convergence in a complete lattice was introduced by Scott to characterize continuous lattices. Here we introduce and study the lim-inf convergence in a partially ordered set. The main result is that for a poset P the lim-inf convergence is topological if and only if P is a continuous poset. A weaker form of lim-inf convergence in posets is also discussed. |
| Keywords: | Lim-inf-convergence Continuous posets Lim-inf2-convergence α-Continuous posets |
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