Sobriety of quantale-valued cotopological spaces
Dexue Zhang
TL;DR
This paper develops a new theory of sobriety for quantale-valued cotopological spaces using fuzzy order and irreducible closed sets, extending classical topological concepts into a fuzzy, algebraic framework.
Contribution
It introduces a novel sobriety concept for quantale-valued cotopological spaces based on fuzzy order and irreducible closed sets, advancing the understanding of fuzzy topology.
Findings
Established a sobriety theory for quantale-valued cotopological spaces.
Linked fuzzy order with irreducible closed sets in the context of sobriety.
Extended classical topological sobriety to a fuzzy, algebraic setting.
Abstract
For each commutative and integral quantale, making use of the fuzzy order between closed sets, a theory of sobriety for quantale-valued cotopological spaces is established based on irreducible closed sets.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFuzzy and Soft Set Theory · Advanced Algebra and Logic · Rough Sets and Fuzzy Logic