论文标题
在$ T_0 $空间的H-索伯空间和H-S-obrification
On H-sober spaces and H-sobrifications of $T_0$ spaces
论文作者
论文摘要
在本文中，我们为$ d $空间，清醒的空间和过滤良好的空间提供了统一的方法，并开发了处理所有这些空间的一般框架。对于子集系统h，建立了H-索伯空间和超级H-索空间的理论，并给出了$ T_0 $空间的H-近距离和超级H-验证的直接构造。因此，所有H-索伯空间的类别都在$ \ mathbf {top} _0 $中反射，并且所有超级h-seber空间的类别在$ \ mathbf {top} _0 $（如果H具有天然属性（称为属性M）（称为属性M）（称为属性M）（称为property M）（称为property M）（称为top} _0）中。结果表明，H-S-obrification保留了$ T_0 $空间的有限产品，而超级H-S-S-S-S-S-S-S-S-S-S-S-S-S-S-0 $ T_0 $空间则保留了$ T_0 $的空间。
In this paper, we provide a uniform approach to $d$-spaces, sober spaces and well-filtered spaces, and develop a general framework for dealing with all these spaces. For a subset system H, the theory of H-sober spaces and super H-sober spaces is established, and a direct construction of the H-sobrifcations and super H-sobrifications of $T_0$ spaces is given. Therefore, the category of all H-sober spaces is reflective in $\mathbf{Top}_0$, and the category of all super H-sober spaces is also reflective in $\mathbf{Top}_0$ if H has a natural property (called property M). It is shown that the H-sobrification preserves finite products of $T_0$ spaces, and the super H-sobrification preserves finite products of $T_0$ spaces if H has property M.
