公开选择
Overt choice
摘要：
我们引入并研究了可数基空间和CoPolish空间的显性选择概念。公开的选择是在一个闭集中产生一个点的任务，该点由什么开集与它相交来指定。我们证明了对于给定的空间，公开的选择是否连续的问题与拓扑完备性概念（如Choquet性质）有关;以及Michael选择定理的变体是否适用于该空间。对于显性选择是不连续的空间，探索由此产生的Weihrauch度是有趣的，这反过来又与空间是否是Frechet-Urysohn有关。
英文摘要：
We introduce and study the notion of overt choice for countably-based spaces and for CoPolish spaces. Overt choice is the task of producing a point in a closed set specified by what open sets intersect it. We show that the question of whether overt choice is continuous for a given space is related to topological completeness notions such as the Choquet-property; and to whether variants of Michael's selection theorem hold for that space. For spaces where overt choice is discontinuous it is interesting to explore the resulting Weihrauch degrees, which in turn are related to whether or not the space is Frechet-Urysohn.
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