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Research Article Open access CC BY 3.0

A Note on Quasicontinuous Domains

Qingyu He, Luoshan Xu

Journal of Advances in Mathematics and Computer Science · pp. 3171–3178 · Published 4 Sep 2014

10.9734/BJMCS/2014/12840

Abstract

In this note, the quasicontinuity of a dcpo and its principal ideals/filters are considered. It is shown that every principal ideal, as a subposet, in a quasicontinuous domain is also a quasicontinuous domain. A dcpo is quasicontinuous if every principal ideal is quasicontinuous and it has finitely many maximal elements. For a bc-domain being quasicontinuous, the requirement of directedness of the approximation family of each element can be omitted.

Quasicontinuous domain principal ideal Scott topology semilattice.

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