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arXiv · 2306.16806

Free dcpo-algebras via directed spaces

Yuxu Chen·Hui Kou·Zhenchao Lyu
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Abstract

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.

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Yuxu Chen, Hui Kou, Zhenchao Lyu. 2023-06-29. Free dcpo-algebras via directed spaces. https://arxiv.org/abs/2306.16806

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