U K -Admitting DCPOS Need not be Sober
U K -Admitting DCPOS Need not be Sober
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DOI：
10.1007/978-94-010-0654-5_3
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
H. Kou
中科院分区：
文献类型：
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作者：
H. Kou
每个具有Scott拓扑的sober dcpop都是Uk-容许的，即对每个Scott开集U和P的紧致上集的滤子族F，<$F <$U对某个K <$F蕴涵K <$U。本文构造了一个不清醒的aUK-接纳dcpo的例子，从而否定了Heckmann在1991年提出的一个公开问题。此外，我们证明了，对于每一个局部紧dcpo，UK-admitting等价于清醒。
Every sober dcpoPwith the Scott topology isUk-admitting, that is, for every Scott open setUand a filtered familyFof compact upper sets ofP,⋂F⊂UimpliesK⊂Ufor someK⊂F. In this note, we construct an example of aUk-admitting dcpo which is not sober, thus giving a negative answer to an open problem posed by Heckmann in 1991. Moreover, we prove that for every locally compact dcpo,Uk-admitting is equivalent to sober.