论文标题
由单调收敛类确定的拓扑空间的笛卡尔封闭核心式子类别
Cartesian closed coreflective subcategories of topological spaces determined by monotone convergence classes
论文作者
论文摘要
我们介绍了操作$ \ MATHCAL {P} $和$ \ MATHCAL {P} $ - 确定空间的概念。显示出一个类别是$ \ bf top $的核心完整子类别。 $ \ MATHCAL {P} $ - 确定的空间。作为$ \ Mathcal {p} $确定的空间的具体示例，详细研究了由单调收敛类确定的几类拓扑空间。通过$ \ mathbb {c} $生成的空间的工具，统一显示了这些示例的类别$ \ m rathcal {p} $ - 确定的空间都是笛卡尔封闭的。此外，域理论中某些类别的指数对象和分类产品与$ \ bf dtop $（定向空间的类别）密切相关。
We introduce the notion of an operation $\mathcal{P}$ and a $\mathcal{P}$-determined space. It is shown that a category is a coreflective full subcategory of $\bf Top$ if and only if it is equal to $\bf Top_{\mathcal{P}}$ for some idempotent and consistent operation $\mathcal{P}$, where $\bf Top_{\mathcal{P}}$ is the category of all $\mathcal{P}$-determined spaces. As concrete examples of $\mathcal{P}$-determined spaces, several classes of topological spaces determined by monotone convergence classes are investigated in detail. By the tool of $\mathbb{C}$-generated spaces, it is shown uniformly that categories of these examples of $\mathcal{P}$-determined spaces are all cartesian closed. Moreover, the exponential objects and categorical products of some categories in domain theory are shown to be closely related to those of $\bf DTop$, the category of directed spaces.
