Abstract
This paper concerns algebraic L-domains. Main results are: (1) All the compact elements of an algebraic L-domain forms an L-cusl; (2) An algebraic L-domain equipped with the Scott topology is the sobrification of the set of all compact elements equipped with the Alexandrov topology; (3) The ideal completion of an L-cusl is an algebraic L-domain. (4) It is also proved that with proper concepts of L-cusl embeddings and projection pairs, the category of algebraic L-domains and projection pairs is equivalent to the category of L-cusls and L-cusl embeddings. Mathematics Subject Classification: 06A11; 18A40; 54H10
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