The Answer to a Problem Posed by Zhao and Ho
The Answer to a Problem Posed by Zhao and Ho
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DOI：
10.1007/s10114-018-7535-6
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发表时间：
2018-09
期刊：
影响因子：
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通讯作者：
Bin Zhao;Jing Lu;K. Wang
中科院分区：
文献类型：
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作者：
Bin Zhao;Jing Lu;K. Wang
赵和Ho在最近的一篇论文中问到，对于每个T0空间X，Kb(X)(X的所有存在上界的不可约闭集的集合)是否是X在Keimel和Lawson意义下的规范k-有界软化。在这篇文章中，我们构造了一个反例来给出否定的答案。我们还考虑了T0空间范畴Top0的子范畴Top0，并证明了k-有界清醒空间范畴KBSOB是范畴κ的完全反射子范畴KBSOB是范畴Topκ的完全反射子范畴。
Zhao and Ho asked in a recent paper that for eachT0spaceX, whetherKB(X) (the set of all irreducible closed sets ofXwhose suprema exist) is the canonical k-bounded sobrification ofXin the sense of Keimel and Lawson. In this paper, we construct a counterexample to give a negative answer. We also consider the subcategoryTopκof the categoryTop0ofT0spaces, and prove that the categoryKBSobof k-bounded sober spaces is a full reflective subcategory of the categoryKBSobof k-bounded sober spaces is a full reflective subcategory of the categoryTopκ.