代数L-domain的表示定理及其相关范畴性质

引人局部条件并半格(简记为L-cusl)及其理想完备化等概念．证明了：任一代数L-domain的紧元集是L-cusl，任一代数L-domain是其紧元集赋予A1exandrov拓扑时的Sober化；任一L-cusl的理想完备化是代数L-domain，从而得到了代数L-domain的表示定理．还证明了Scott连续映射为态射的代数L-domain范畴为L-cusl与单调映射作成的范畴的反射于范畴．

REPRESENTATION THEOREM OF ALGEBRAIC L-DOMAINS AND SOME PROPERTIES OF RELEVANT CATEGORIES

This paper introduces the new concepts of locally conditional upper semilattice (in short, L-cusl) and their ideal completions. It is proved that the set of compact elements in an algebraic L-domain is an L-cusl, that algebraic L-domains equipped with Scott topology are the soberification of their sets of compact elements equipped with pseudoScott topology and that the ideal completion of an L-cusl is an algebraic L-domain, obtaining a representation theorem for algebraic L-domains. It is also proved that the category of algebraic L-domains with Scott continuous functions as morphisms is a reflective subcategory of the category of L-cusls and monotone maps.