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A note on the category of c-spaces
Z. Lyu, X. Xie, H. Kou
We prove that the category of c-spaces with continuous maps is not cartesian closed. As a corollary the category of locally finitary compact spaces with continuous maps is also not…
Free algebras over directed spaces
Yuxu Chen, Hui Kou
Directed spaces are natural topological extensions of dcpos in domain theory and form a cartesian closed category. In order to model nondeterministic semantics, the power structure…
-convergence and locally hypercompact spaces
Yuxu Chen, Hui Kou
In this paper, we give a topological version of Scott convergence theorem for locally hypercompact spaces. We introduce the notion of -convergence on a topol…
Monotone determined spaces via -generated spaces
Yuxu Chen, Hui Kou, Zhenchao Lyu
The category of monotone determined spaces is an extended topological framework for dcpos in domain theory. We first show that monotone determined spaces are exactly the spaces gen…
Power structures of directed spaces
Xiaolin Xie, Yuxu Chen, Hui Kou
Powerdomains in domain theory plays an important role in modeling the semantics of nondeterministic functional programming languages.\ In this paper,\ we extend the notion of power…
The Directed Probabilistic Powerspace
Xiaolin Xie, Hui Kou, Zhenchao Lyu
Probabilistic powerdomain in domain theory plays an important role in modeling the semantics of nondeterministic functional programming languages with probabilistic choice. In this…
Continuity and core compactness of topological spaces
Yuxu Chen, Hui Kou, Zhenchao Lyu
We investigate two approximation relations on a T0 topological space, the n-approximation, and the d-approximation, which are generalizations of the way-below relation on a dcpo. D…