Natural congruences and isomorphism theorems for directed complete partially ordered sets |
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| Authors: | Mojgan Mahmoudi Halimeh Moghbeli Konrad Pióro |
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| Affiliation: | 1.Department of Mathematics,Shahid Beheshti University, G.C.,Tehran,Iran;2.Department of Mathematics, Faculty of Science,University of Jiroft,Jiroft,Iran;3.Department of Mathematics,Shahid Beheshti University,Tehran,Iran;4.Institute of Mathematics,University of Warsaw,Warsaw,Poland |
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| Abstract: | 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. |
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