Strongly Semicontinuous Domains and Semi-FS Domains

الملخص EN

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.