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Hypercontinuous Posets |
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| Authors: | Wenfeng ZHANG and Xiaoquan XU |
| Institution: | Wenfeng ZHANG;Xiaoquan XU;Department of Mathematics, Sichuan University;Department of Mathematics, Jiangxi Normal University; |
| Abstract: | The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent: (1) P is hypercontinuous; (2) the dual of P is generalized completely continuous; (3) the normal completion of P is a hypercontinuous lattice. In addition, the relational representation and the intrinsic characterization of hypercontinuous posets are obtained. |
| Keywords: | Hypercontinuous posets Generalized completely continuous posets Normal completion |
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