# Zhenchao LyuSichuan University | SCU · College of Mathematics

Zhenchao Lyu

Ph.D.

## About

14

Publications

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41

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Introduction

**Skills and Expertise**

## Publications

Publications (14)

We prove that the probabilistic powerdomain of a coherent locally finitary compact T0 space is coherent quasicontinuous. As a result, we obtain a novel proof of Larrecq's and Jung's result in 2014. The main tool for our proof is the weak topology on the probabilistic powerdomain. In addition, we show that a dcpo L is continuous (resp., quasicontinu...

We study $G_\delta$ subspaces of continuous dcpos, which we call domain-complete spaces, and $G_\delta$ subspaces of locally compact sober spaces, which we call LCS-complete spaces. Those include all locally compact sober spaces-in particular, all continuous dcpos-, all topologically complete spaces in the sense of \v{C}ech, and all quasi-Polish sp...

We prove that the Smyth powerspace Q(X) of a topological space X is core-compact if and only if X is locally compact. As a straightforward consequence we obtain that the Smyth powerspace construction does not preserve core-compactness generally.

In this paper, we investigate the properties of almost algebraic domains introduced by G. Hamrin and V. Stoltenberg-Hansen in 2006. We introduce a notion of M-closed basis and define a new class of domains, called ωAML-domains, which are continuous L-domains endowed with countable, almost algebraic, and M-closed bases. The main result of this paper...

We give a construction of the free dcpo-cone over any dcpo. There are two steps for getting this result. Firstly, we extend the notion of power domain to directed spaces which are equivalent to $T_0$ monotone-determined spaces introduced by Erné, and we construct the probabilistic powerspace of the monotone determined space, which is defined as a f...

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 $\Sigma L$, on the context of directed spaces, are exactly the free dcpo-algebras over dcpo $L$, which reveals the close connection between directed powerspaces and...

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 cartesian closed.

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. Different kinds of continuous spaces are defined by the two approximations and are all shown to be directed spaces. We show that the continuity of a directed space is very...

Probabilistic powerdomain in domain theory plays an important role in modeling the semantics of nondeterministic functional programming languages with probabilistic choice. In this paper, we extend the notion of powerdomain to directed spaces, which is equivalent to the notion of the T0 monotone-determined space [4]. We construct the probabilistic...

We prove that the Smyth powerspace QS(X) of a topological space X is core-compact if and only if X is locally compact. As a straightforward consequence, we obtain that the Smyth powerspace construction does not preserve core-compactness generally. Besides, we prove that QS(X) is consonant implies that X is consonant and conversely that the Smyth po...

For a poset P, let σ(P) and Γ(P) respectively denote the lattice of its Scott open subsets and Scott closed subsets ordered by inclusion, and set ΣP=(P,σ(P)). In this paper, we discuss the lower Vietoris topology and the Scott topology on Γ(P) and give some sufficient conditions to make the two topologies equal. We build an adjunction between σ(P)...

For a poset $P$, let $\sigma(P)$ and $\Gamma(P)$ respectively denote the lattice of its Scott open subsets and Scott closed subsets ordered by inclusion, and set $\Sigma P=(P,\sigma(P))$. In this paper, we discuss the lower Vietoris topology and the Scott topology on $\Gamma(P)$ and give some sufficient conditions to make the two topologies equal....

We study Gδ subspaces of continuous dcpos, which we call domain-complete spaces, and Gδ subspaces of locally compact sober spaces, which we call LCS-complete spaces. Those include all locally compact sober spaces—in particular, all continuous dcpos—, all topologically complete spaces in the sense of Čech, and all quasi-Polish spaces—in particular,...