Zobrazeno 1 - 10
of 122
pro vyhledávání: '"Xi, Xiaoyong"'
We construct two dcpo's whose Scott spaces are sober, but the Scott space of their order product is not sober. This answers an open problem on the sobriety of Scott spaces. Meantime, we show that if $M$ and $N$ are special type of sober complete latt
Externí odkaz:
http://arxiv.org/abs/2408.08587
A topological space has a domain model if it is homeomorphic to the maximal point space $\mbox{Max}(P)$ of a domain $P$. Lawson proved that every Polish space $X$ has an $\omega$-domain model $P$ and for such a model $P$, $\mbox{Max}(P)$ is a $G_{\de
Externí odkaz:
http://arxiv.org/abs/2305.04012
Publikováno v:
Electronic Notes in Theoretical Informatics and Computer Science, Volume 2 - Proceedings of ISDT 9 (March 21, 2023) entics:10392
The open well-filtered spaces were introduced by Shen, Xi, Xu and Zhao to answer the problem whether every core-compact well-filtered space is sober. In the current paper we explore further properties of open well-filtered spaces. One of the main res
Externí odkaz:
http://arxiv.org/abs/2211.16133
In this paper, we mainly discuss some basic properties of Scott power spaces. For a $T_0$ space $X$, let $\mathsf{K}(X)$ be the poset of all nonempty compact saturated subsets of $X$ endowed with the Smyth order. It is proved that the Scott power spa
Externí odkaz:
http://arxiv.org/abs/2207.08720
The study of the sobriety of Scott spaces has got an relative long history in domain theory. Lawson and Hoffmann independently proved that the Scott space of every continuous directed complete poset (usually called domain) is sober. Johnstone constru
Externí odkaz:
http://arxiv.org/abs/2205.00250
Keimel and Lawson proposed a set of conditions for proving a category of topological spaces to be reflective in the category of all T0 spaces. These conditions were recently used to prove the reflectivity of the category of all well-filtered spaces.
Externí odkaz:
http://arxiv.org/abs/2110.01138
We investigate some versions of $d$-space, well-filtered space and Rudin space concerning various countability properties. The main results include: (i) if the sobrification of a $T_0$ space $X$ is first-countable, then $X$ is an $\omega$-Rudin space
Externí odkaz:
http://arxiv.org/abs/2008.11023
Publikováno v:
Logical Methods in Computer Science, Volume 16, Issue 4 (December 18, 2020) lmcs:6041
We introduce and study a new class of $T_0$ spaces, called open well-filtered spaces. The main results we proved include (1) every well-filtered space is an open well-filtered space; (2) every core-compact open well-filtered space is sober. As an imm
Externí odkaz:
http://arxiv.org/abs/2001.07397
We first introduce and study two new classes of subsets in $T_0$ spaces - $\omega$-Rudin sets and $\omega$-well-filtered determined sets lying between the class of all closures of countable directed subsets and that of irreducible closed subsets, and
Externí odkaz:
http://arxiv.org/abs/1911.13201
We first introduce and study two new classes of subsets in $T_0$ spaces - Rudin sets and $\wdd$ sets lying between the class of all closures of directed subsets and that of irreducible closed subsets. Using such subsets, we define three new types of
Externí odkaz:
http://arxiv.org/abs/1909.09303