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Strongly semicontinuous domains and semi-FS domains.

Research paper by Qingyu Q He, Luoshan L Xu

Indexed on: 13 Sep '14Published on: 13 Sep '14Published in: TheScientificWorldJournal



Abstract

We are mainly concerned with some special kinds of semicontinuous domains and relationships between them. New concepts of strongly semicontinuous domains, meet semicontinuous domains and semi-FS domains are introduced. It is shown that a dcpo L is strongly semicontinuous if and only if L is semicontinuous and meet semicontinuous. It is proved that semi-FS domains are strongly semicontinuous. Some interpolation properties of semiway-below relations in (strongly) semicontinuous bc-domains are given. In terms of these properties, it is proved that strongly semicontinuous bc-domains, in particular strongly semicontinuous lattices, are all semi-FS domains.