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Strongly semicontinuous domains and semi-FS domains
1Department of Mathematics, Yangzhou University, Yangzhou 225002, China.
Thescientificworldjournal
|September 13, 2014
Summary
This study introduces new concepts for semicontinuous domains, proving that strongly semicontinuous domains are equivalent to being both semicontinuous and meet semicontinuous, and are also semi-FS domains.
Area of Science:
- Domain theory
- Order theory
- Theoretical computer science
Background:
- Semicontinuous domains are fundamental in domain theory.
- Understanding their properties is crucial for applications in logic and computer science.
Purpose of the Study:
- Introduce and define strongly semicontinuous domains, meet semicontinuous domains, and semi-FS domains.
- Investigate the relationships between these domain types.
- Establish characterizations and properties of these domains.
Main Methods:
- Introduction of new domain concepts.
- Proof of equivalences and implications using theoretical methods.
- Analysis of interpolation properties of semiway-below relations.
Main Results:
- A domain L is strongly semicontinuous if and only if it is both semicontinuous and meet semicontinuous.
- All semi-FS domains are shown to be strongly semicontinuous.
- Strongly semicontinuous bc-domains (and lattices) are proven to be semi-FS domains.
Conclusions:
- The study provides a comprehensive understanding of various semicontinuous domains.
- Established equivalences and properties offer new insights into domain theory.
- The findings contribute to the theoretical foundations of areas relying on domain structures.
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