Meet-continuity andlocally compact sober dcpos

[摘要] In this thesis, we investigate meet-continuity over dcpos. We give different equivalent descriptions ofmeet-continuous dcpos, among which an important characterisation is given via forbiddensubstructures. By checking the function space of such substructures we prove, as a central contribution,that any dcpo with a core-compact function space must be meet-continuous. As an application , thisresult entails that any cartesian closed full subcategory of quasicontinuous domains consists ofcontinuous domains entirely. That is to say , both the category of continuous domains and that ofquasicontinuous domains share the same cartesian closed full subcategories.Our new characterisation of meet-continuous dcpos also allows us to say more about full subcategoriesof locally compact sober dcpos which are generalisations of quasicontinuous domains. Afterdeveloping some theory of characterising coherence and bicompleteness of dcpos, we conclude thatany cartesian closed full subcategory of pointed locally compact sober dcpos is entirely contained inthe category of stably compact dcpos or that of L-dcpos. As a by-product, our study of coherence of dcpos enables us to characterise Lawson-compactness overarbitrary dcpos.

[发布机构] University:University of Birmingham;Department:School of Computer Science

[关键词] Q Science;QA Mathematics