| On the Existence of Suprema of Infinite Many Elements in a Riesz Space |
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| 作者姓名： | 荣喜民 熊洪允 |
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| 作者单位： | Department of Mathematics Tianjin University，Department of Mathematics Tianjin University |
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| 摘 要： | <正> Let E be a Riesz space with a disjoint system {u_i :i∈I}. We denote by E_i the principal band generated by u_i(i∈I). A necessary and sufficient condition is found in this paper under which sup{X_i:i∈I} exists in E for every x_i∈E (i∈I).
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On the Existence of Suprema of Infinite Many Elements in a Riesz Space |
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| Abstract: | Let E be a Riesz space with a disjoint system {u_i :i∈I}. We denote by E_i the principal band generated by u_i(i∈I). A necessary and sufficient condition is found in this paper under which sup{X_i:i∈I} exists in E for every x_i∈E (i∈I). |
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