AI 中文总结
针对迷人空间的D空间问题，通过定义Obs_cc(Y,B)与H，证明X是D空间等价于H是，还给出含紧覆盖数、优超数d的充分条件，实现问题归约。
AI 中文摘要
设X是具有林德洛夫Σ核Y的迷人空间，B是Y在X中的闭包。我们证明：每个迷人空间是否为D空间的问题，可先归约至密核情形，再归约至闭核。定义Obs_cc(Y,B)为B中Y以外的边界点x的集合，满足对X中x的任意开邻域U，U与Y的交集都不是可数紧的；令H为Obs_cc(Y,B)在B中的闭包。我们证明H与B\backslash Y的交集恰好是Obs_cc(Y,B)，且核心归约定理表明：X是D空间当且仅当H是D空间。还证明充分条件：若存在B\backslash Y中的闭集S，其紧覆盖数小于优超数d，且B\backslash Y\backslash S的每个点都在X中有开邻域U，使得U与Y的交集是可数紧的，则X是D空间。
英文摘要
Let X be a charming space with a Lindelof Sigma kernel Y, and let B be the closure of Y in X. We show that the question whether every charming space is a D-space can be reduced first to the dense-kernel case and then to a closed core. We define Obs_cc(Y,B) as the set of boundary points x in B minus Y such that, for every open neighborhood U of x in X, the intersection of U and Y is not countably compact, and let H be the closure of Obs_cc(Y,B) in B. We prove that the intersection of H with B minus Y is exactly Obs_cc(Y,B), and our main reduction theorem shows that X is a D-space if and only if H is. We also prove the following sufficient condition. If there is a closed set S contained in B minus Y with compact covering number less than the dominating number d, such that every point of B minus Y minus S has an open neighborhood U in X for which the intersection of U and Y is countably compact, then X is a D-space.
Comments32 pages
