The concept of locally strong compactness on domains is generalized to general topological spaces. It is proved that for each distributive hypercontinuous lattice L, the space SpecL of nonunit prime elements endowed w...The concept of locally strong compactness on domains is generalized to general topological spaces. It is proved that for each distributive hypercontinuous lattice L, the space SpecL of nonunit prime elements endowed with the hull-kernel topology is locally strongly compact, and for each locally strongly compact space X, the complete lattice of all open sets O(X) is distributive hypercontinuous. For the case of distributive hyperalgebraic lattices, the similar result is given. For a sober space X, it is shown that there is an order reversing isomorphism between the set of upper-open filters of the lattice O(X) of open subsets of X and the set of strongly compact saturated subsets of X, which is analogous to the well-known Hofmann-Mislove Theorem.展开更多
In the new century, the Communist Party of China has successively launched three campaigns of intra-Party intensive education： the important thought of the Three Represents education campaign in rural areas, the Part...In the new century, the Communist Party of China has successively launched three campaigns of intra-Party intensive education： the important thought of the Three Represents education campaign in rural areas, the Party-wide education campaign to maintain the vanguard nature of Party members mainly by putting the important thought of the Three Represents into practice and the campaign to intensively study and apply the Scientific Outlook on Development. Through these activities, the majority of Party members and cadres have received profound Marxist education, further deepening their understanding of the important thought of the Three Represents. The campaigns advanced the great project of Party building at a new historical starting point, and are thus of inspiring significance.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 10331010, 10861007)the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 2007B14)+2 种基金the Jiangxi Provincial Natural Science Foundation of China (Nos. 0411025, 2007GZS0179)the Foundation of the Education Department of Jiangxi Province (No. GJJ08162)the Doctoral Fund of Jiangxi Normal University
文摘The concept of locally strong compactness on domains is generalized to general topological spaces. It is proved that for each distributive hypercontinuous lattice L, the space SpecL of nonunit prime elements endowed with the hull-kernel topology is locally strongly compact, and for each locally strongly compact space X, the complete lattice of all open sets O(X) is distributive hypercontinuous. For the case of distributive hyperalgebraic lattices, the similar result is given. For a sober space X, it is shown that there is an order reversing isomorphism between the set of upper-open filters of the lattice O(X) of open subsets of X and the set of strongly compact saturated subsets of X, which is analogous to the well-known Hofmann-Mislove Theorem.
文摘In the new century, the Communist Party of China has successively launched three campaigns of intra-Party intensive education： the important thought of the Three Represents education campaign in rural areas, the Party-wide education campaign to maintain the vanguard nature of Party members mainly by putting the important thought of the Three Represents into practice and the campaign to intensively study and apply the Scientific Outlook on Development. Through these activities, the majority of Party members and cadres have received profound Marxist education, further deepening their understanding of the important thought of the Three Represents. The campaigns advanced the great project of Party building at a new historical starting point, and are thus of inspiring significance.
