A construction of free dcpo-cones
A construction of free dcpo-cones
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DOI：
10.1017/s0960129523000427
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发表时间：
2024-01
期刊：
影响因子：
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通讯作者：
Yuxu Chen;H. Kou;Zhenchao Lyu;Xiaolin Xie
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文献类型：
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作者：
Yuxu Chen;H. Kou;Zhenchao Lyu;Xiaolin Xie
给出了任意dcpo上自由dcpo-锥的一个构造。有两个步骤可以得到这个结果。首先，我们将幂域的概念推广到与Erné引入的单调确定空间等价的有向空间，并构造了单调确定空间的概率幂空间，定义单调确定空间为自由单调确定锥。其次，利用Scott拓扑，得到了dcpo上自由单调确定锥的D-完备化。此外，我们还证明了一般情况下任何dcpo的赋值幂域都不是自由dcpo-锥。
We give a construction of the free dcpo-cone over any dcpo. There are two steps for getting this result. Firstly, we extend the notion of power domain to directed spaces which are equivalent to $T_0$ monotone-determined spaces introduced by Erné, and we construct the probabilistic powerspace of the monotone determined space, which is defined as a free monotone determined cone. Secondly, we take D-completion of the free monotone determined cone over the dcpo with its Scott topology. In addition, we show that generally the valuation power domain of any dcpo is not the free dcpo-cone.