论文标题
某些弱清醒的空间的非反射类别
Non-reflective categories of some kinds of weakly sober spaces
论文作者
论文摘要
Erné削弱了清醒的概念，以扩展清醒的空间和局部超紧张的空间的理论，以至于缺失了定向联接的情况，并引入和讨论了三种非偷偷空间：切断的空间，弱清醒的空间和准室空间。 Xu，Shen，XI和Zhao介绍了其他三种非索伯空间，即$ \ Mathsf {dc} $ space，$ \ mathsf {rd} $ space和$ \ Mathsf {wd} $ space。所有这六种空间都比清醒的空间弱。在本文中，结果表明，所有$ \ mathsf {dc} $空间的类别都不是所有$ \ mathsf {rd} $ spaces中的所有类别，所有$ \ \ \ \ m varssf {wd} $ spaces中的所有类别，所有$ cobober空间的空间和所有cut cut space的空间都在所有$ cut space cut的空间中都反映了所有$的$。
Erné weakened 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 and discussed three kinds of non-sober spaces: cut spaces, weakly sober spaces, and quasisober spaces. Three other kinds of non-sober spaces, namely $\mathsf{DC}$ space, $\mathsf{RD}$ space and $\mathsf{WD}$ space, were introduced and investigated by Xu, Shen, Xi and Zhao. All these six kinds of spaces are strictly weaker than sober spaces. In this paper, it is shown that none of the category of all $\mathsf{DC}$ spaces, that of all $\mathsf{RD}$ spaces, that of all $\mathsf{WD}$ spaces, that of all quasisober spaces, that of all weakly spaces and that of all cut spaces is reflective in the category of all $T_0$ spaces with continuous mappings.
