Natural congruences and isomorphism theorems for directed complete partially ordered sets
Natural congruences and isomorphism theorems for directed complete partially ordered sets
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DOI：
10.1007/s00012-017-0424-5
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发表时间：
2017-01
影响因子：
0.6
通讯作者：
M. Mahmoudi;Halimeh Moghbeli;K. Pióro
中科院分区：
文献类型：
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作者：
M. Mahmoudi;Halimeh Moghbeli;K. Pióro
有向完全偏序集（简称dcpos）在领域理论中发挥着重要作用。本文的目的是描述 dcpos 的自然同余特征。我们还表明，dcpo 映射的内核，即 dcpos 之间的定向连接保留映射不一定是自然的 dcpo 同余。然后我们表征 dcpo 映射，其内核是自然 dcpo 同余。最后，我们证明了 dcpo 映射的分解和同构定理。
Directed complete partially ordered sets (dcpos, for short) play an important role in domain theory. The aim of this paper is to characterise natural congruences of dcpos. We also show that the kernels of dcpo maps, that is, directed join-preserving maps between dcpos are not necessarily natural dcpo congruences. Then we characterise dcpo maps whose kernels are natural dcpo congruences. Finally, we prove the Decomposition and Isomorphism Theorems for dcpo maps.