9 papers
The sobriety for locally compact dcpos
Zhengmao He, Yujing Zhang
In this paper, we focus on an open problem whether every locally compact dcpo is sober for the Scott topology. Specifically, we obtain two sufficient conditions for answering this…
The product of two Scott sober complete lattices is not always Scott sober
Zhengmao He
In this paper, we obtain two complete lattices that are sober with respect to the Scott topology, whereas the Scott space of their product is not a sober space. Thus, we answer a q…
Sobriety of Scott topologies under countability conditions
Zhengmao He, Zhaochen Dong, Kaiyun Wang
In this paper, we focus on the sobriety of the Scott topology in countable case. Specifically, we show that: (1) every meet-continuous core-compact countable dcpo is sober with res…
Applications of sequential spaces to Smyth power spaces and sober spaces
Zhengmao He
Recently, in the study of topological properties in Domain theory, the first countable spaces and Frechet-Urysohn spaces receive close attention and are frequently employed. In thi…
Two problems of SI-compact spaces
Zhengmao He
Zhao and Ho use the irreducible open cover family respected with the Scott topology to introduce the SI-compactness. It has been proved that the SI-compactness is strictly stronger…
A new method for constructing a compact and non SI-compact space
Zhengmao He, Bin Zhao
In this paper, we provide a new method for constructing a compact and non SI-compact space and thus give a new answer for the question posed by Zhao and Ho. Using this method, we f…
When do weakly first-countable spaces and the Scott topology of open set lattice become sober?
Zhengmao He
In this paper, we investigate the sobriety of weakly first-countable spaces and give some sufficient conditions that the Scott topologies of the open set lattices are sober. The ma…
ArrayBot: Reinforcement Learning for Generalizable Distributed Manipulation through Touch
Zhengrong Xue, Han Zhang, Jingwen Cheng +5
We present ArrayBot, a distributed manipulation system consisting of a array of vertically sliding pillars integrated with tactile sensors, which can simultaneously…
Some problems about co-consonance of topological spaces
Zhengmao He, Bin Zhao
In this paper, we first prove that the retract of a consonant space (or co-consonant space) is consonant (co-consonant). Using this result, some related results have obtained. Simu…