论文标题
在$ \ mathbf {k} $ - Scott Space的反射
On $\mathbf{K}$-reflections of Scott spaces
论文作者
论文摘要
In this paper, for a full subcategory $\mathbf{K}$ of the category of all $T_0$ spaces with continuous mappings, we investigate the questions under what conditions the $\mathbf{K}$-reflection of a Scott space is still a Scott space and under what conditions the Scott $\mathbf{K}$-completion of a poset exists. $ \ mathbf {k} $的一些必要和充分的条件 - 对斯科特空间的反映，分别建立了poset的Scott $ \ Mathbf {k} $的存在。结果表明，约翰斯通空间的so缩和过滤的反射都不是斯科特空间。还讨论了$ \ mathbf {k} $ - ALEXANDROFF空间的反射和$ \ Mathbf {K} $ - POSETS的完成。
In this paper, for a full subcategory $\mathbf{K}$ of the category of all $T_0$ spaces with continuous mappings, we investigate the questions under what conditions the $\mathbf{K}$-reflection of a Scott space is still a Scott space and under what conditions the Scott $\mathbf{K}$-completion of a poset exists. Some necessary and sufficient conditions for the $\mathbf{K}$-reflection of a Scott space to be a Scott space and for the existence of Scott $\mathbf{K}$-completion of a poset are established, respectively. It is shown that neither the sobrification nor the well-filtered reflection of the Johnstone space is a Scott space. The $\mathbf{K}$-reflections of Alexandroff spaces and the $\mathbf{K}$-completions of posets are also discussed.
