2023/06/29 by Yuxu Chen, Chen, Yuxu, Hui Kou +3
Computer Science · Mathematics · Decision Sciences · #Advanced Algebra and Logic #Advanced Topics in Algebra #Fuzzy and Soft Set Theory
paper · pdf · doi:10.48550/arxiv.2306.16806
Directed spaces are natural topological extensions of dcpos in domain theory and form a cartesian closed category. We will show that the D-completion of free algebras over a Scott space ΣL, on the context of directed spaces, are exactly the free dcpo-algebras over dcpo L, which reveals the close connection between directed powerspaces and powerdomains. By this result, we provide a topological representation of upper, lower and convex powerdomains of dcpos uniformly.