Several L-domain Of Operation

In this thesis, we investigate the characterizations of L-domains, and some hereditary properties, sum, product and continuous func-tion spaces of L-domains. The content of this thesis are as followings:The first part of this paper, we introduce the characterizations of L-domains. Then we define the subspaces of L-domain. We show that the scott open sets and scott closed sets of L-domains are subspaces of L-domains.On the second part, we define some sums of L-domains with scott continuous functions. We show that L-domains are preserved by some sums of L-domains with scott continuous functions. Then we show that the coproduct of the category of L-domains is the disjoint sum, and the coproduct of the category of L-domains which has the smallest element is the coalesced sum.On the third part, we investigate the cartesian product of L-domains. For a family of L-domains which have the smallest elements we show that the cartesian product of a family of L-domains is still an L-domain. Finally, we prove that the continuous function spaces of L-domains are still L-domains.