On some kinds of weakly sober spaces
General Topology
2019-07-16 v1
Abstract
In \cite{E_2018}, Ern\'e relaxed the concept of sobriety in order to extend the theory of sober spaces and locally hypercompact spaces to situations where directed joins were missing, and introduced three kinds of non-sober spaces: cut spaces, weakly sober spaces, and quasisober spaces. In this paper, their basic properties are investigated. It is shown that some properties which are similar to that of sober spaces hold and others do not hold.
Keywords
Cite
@article{arxiv.1907.06316,
title = {On some kinds of weakly sober spaces},
author = {Xinpeng Wen and Xiaoquan Xu},
journal= {arXiv preprint arXiv:1907.06316},
year = {2019}
}