5 citations · 22 across the 32 of their papers we have counts for
28 papers · 1 filter
Characterization of -spaces for quasi-liminf convergence being topological
Xinpeng Wen, Xiaoquan Xu
The authors' primary goal in this paper is to extend some important results related to the liminf-convergence and -convergence in domain theory to the setting of $T_0…
On strong -spaces
Xinpeng Wen, Meng Bao, Xiaoquan Xu
In this paper, we mainly investigate some basic properties of strong -spaces. It is shown that the property of being a strong -space is closed-hereditary, saturated-hereditar…
On three problems about well-filteredness of -spaces
Xiaoquan Xu, Xinpeng Wen
In this paper, we show that there is a countable Noetherian complete lattice and an order-compatible -topology on such that is not well-filtered, and there…
Some new results on well-filteredness of -spaces
Xiaoquan Xu
For a -space , let be the poset of nonempty compact saturated sets of with the reverse inclusion order. The space is said to have property Q if it satisfies…
On sobriety of Scott topology on dcpos
Xiaoquan Xu
In this paper, we mainly investigate the conditions under which the Scott topology on the product of two posets is equal to the product of the individual Scott topologies and under…
-quasicontinuous spaces
Xiaojun Ruan, Xiaoquan Xu
In this paper, as a common generalization of -continuous spaces and -quasicontinuous posets, we introduce the concepts of -quasicontinuous spaces and $\mathc…
On Scott power spaces
Xiaoquan Xu, Xinpeng Wen, Xiaoyong Xi
In this paper, we mainly discuss some basic properties of Scott power spaces. For a space , let be the poset of all nonempty compact saturated subsets of $…
On some kinds of factorizable topological groups
Meng Bao, Xiaoquan Xu
Based on the concepts of -factorizable topological groups and -factorizable topological groups, we introduce four classes of factorizabilities on topologic…
On Function Spaces Related to H-sober Spaces
Meng Bao, Xiaoyuan Zhang, Xiaoquan Xu
In this paper, we mainly study the function spaces related to H-sober spaces. For an irreducible subset system H and spaces and , it is proved that is H-sober if…
Quotient spaces with strong subgyrogroups
Meng Bao, Xuewei Ling, Xiaoquan Xu
In this paper, we mainly investigate the quotient spaces G/H when G is a strongly topological gyrogroup and H is a strong subgyrogroup of G. It is shown that if G is a strongly top…
A supplement on feathered gyrogroups
Meng Bao, Xuewei Ling, Xiaoquan Xu
A topological gyrogroup is a gyrogroup endowed with a topology such that the binary operation is jointly continuous and the inverse mapping is also continuous. It is shown that eac…
A class of quotient spaces in strongly topological gyrogroups
Meng Bao, Jie Wang, Xiaoquan Xu
Quotient space is a class of the most important topological spaces in the research of topology. In this paper, we show that if G is a strongly topological gyrogroup with a symmetri…
Topological gyrogroups with Frechet-Urysohn property and omega^{omega}-base
Meng Bao, Xiaoyuan Zhang, Xiaoquan Xu
The concept of topological gyrogroups is a generalization of a topological group. In this work, ones prove that a topological gyrogroup G is metrizable iff G has an ωω-base and G i…
The strong Pytkeev property and strong countable completeness in (strongly) topological gyrogroups
Meng Bao, Xiaoyuan Zhang, Xiaoquan Xu
A topological gyrogroup is a gyrogroup endowed with a topology such that the binary operation is jointly continuous and the inverse mapping is also continuous. In this paper, it is…
Strongly Topological Gyrogroups and Quotient With Respect to L-subgyrogroups
Meng Bao, Xuewei Ling, Xiaoquan Xu
In this paper, some generalized metric properties in strongly topological gyrogroups are studied.
Separability in (strongly) topological gyrogroups
Meng Bao, Xiaoyuan Zhang, Xiaoquan Xu
Separability is one of the most basic and important topological properties. In this paper, the separability in (strongly) topological gyrogroups is studied. It is proved that every…
-Rudin spaces, well-filtered determined spaces and first-countable spaces
Xiaoquan Xu, Chong Shen, Xiaoyong Xi +1
We investigate some versions of -space, well-filtered space and Rudin space concerning various countability properties. The main results include: (i) if the sobrification of a $…
Some open problems on well-filtered spaces and sober spaces
Xiaoquan Xu, Dongsheng Zhao
In the past few years, the research on sober spaces and well-filtered spaces has got some breakthrough progress. In this paper, we shall present a brief summarising survey on some…
On H-sober spaces and H-sobrifications of spaces
Xiaoquan Xu
In this paper, we provide a uniform approach to -spaces, sober spaces and well-filtered spaces, and develop a general framework for dealing with all these spaces. For a subset s…
Coincidence of the upper Vietoris topology and the Scott topology
Xiaoquan Xu, Zhongqiang Yang
For a space , let $\mk (X)$ be the poset of all compact saturated sets of with the reverse inclusion order. The space is said to have property Q if for any $K_1, K…
On open well-filtered spaces
Chong Shen, Xiaoyong Xi, Xiaoquan Xu +1
We introduce and study a new class of spaces, called open well-filtered spaces. The main results we proved include (1) every well-filtered space is an open well-filtered spac…
First countability, -well-filtered spaces and reflections
Xiaoquan Xu, Chong Shen, Xiaoyong Xi +1
We first introduce and study two new classes of subsets in spaces - -Rudin sets and -well-filtered determined sets lying between the class of all closures of countable…
A direct approach to -reflections of spaces
Xiaoquan Xu
In this paper, we provide a direct approach to -reflections of spaces. For a full subcategory of the category of all spaces and a space $…
On topological Rudin's lemma, well-filtered spaces and sober spaces
Xiaoquan Xu, Dongsheng Zhao
Based on topological Rudin's Lemma, we investigate two new kinds of sets - Rudin sets and well-filtered determined sets in topological spaces. Using such sets, we formulate a…