Topological representations of distributive hypercontinuous lattices
Topological representations of distributive hypercontinuous lattices
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DOI：
10.1007/s11401-007-0316-7
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发表时间：
2009-02
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影响因子：
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通讯作者：
Xiaoquan Xu;Jinbo Yang
中科院分区：
文献类型：
--
作者：
Xiaoquan Xu;Jinbo Yang
域上局部强紧致性的概念被推广到一般拓扑空间。证明对于每个分布超连续格L，赋予壳核拓扑的非单位素元空间SpecL是局部强紧的，对于每个局部强紧空间X，所有开集(X)的完全格是分布超连续的。对于分配超代数格的情况，给出了类似的结果。对于清醒空间X，证明X的开子集格(X)的上开滤波器集合与X的强紧饱和子集集合之间存在倒序同构，类似于著名的Hofmann-Mislove定理。
The concept of locally strong compactness on domains is generalized to general topological spaces. It is proved that for each distributive hypercontinuous latticeL, the space SpecLof nonunit prime elements endowed with the hull-kernel topology is locally strongly compact, and for each locally strongly compact spaceX, the complete lattice of all open sets(X) is distributive hypercontinuous. For the case of distributive hyperalgebraic lattices, the similar result is given. For a sober spaceX, it is shown that there is an order reversing isomorphism between the set of upper-open filters of the lattice(X) of open subsets ofXand the set of strongly compact saturated subsets ofX, which is analogous to the well-known Hofmann-Mislove Theorem.