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When do abstract bases generate continuous lattices and L-domains

Research paper by Luoshan Xu, Xuxin Mao

Indexed on: 10 Jan '08Published on: 10 Jan '08Published in: Algebra universalis



Abstract

In this note, the new concepts of C-bases (resp., BC-bases, L-bases) which are special kinds of abstract bases are introduced. It is proved that the round ideal completion of a C-basis (resp., BC-basis, L-basis) is a continuous lattice (resp., bc-domain, L-domain). Furthermore, representation theorems of continuous lattices (resp., bc-domains, L-domains) by means of the round ideal completions of C-bases (resp., BC-bases, L-bases) are obtained.