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| Hypercontinuous Posets |
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Citation： |
Wenfeng ZHANG,Xiaoquan XU.Hypercontinuous Posets[J].Chinese Annals of Mathematics B,2015,36(2):195~200 |
| Page view： 2442
Net amount： 1683 |
Authors： |
Wenfeng ZHANG; Xiaoquan XU; |
Foundation： |
the National Natural Science Foundation of China (Nos. 10861007,
11161023), the National Excellent Doctoral Dissertation of China (No. 2007B14), the Ganpo 555 Programme
for Leading Talents of Jiangxi Province, the Natural Science Foundation of Jiangxi Province
(No. 20114BAB201008) and the Fund of Education Department of Jiangxi Province (No. GJJ12657). |
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| 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 |
Classification： |
06B23, 18A40 |
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