关于强良滤空间幂空间与函数空间的一个注记
A note on power spaces and function spaces of strongly well-filtered spaces
- Changsha Normal University（长沙师范学院）
- Hunan University（湖南大学）
- Hebei Normal University（河北师范大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文构造可数局部紧强R空间，其幂空间及函数空间均非强d-空间，否定相关保持性质问题。
AI中文摘要：
强良滤性是良滤性在非豪斯多夫拓扑和域论中自然出现的一种细化。本文构造了一个可数的局部紧强R空间X，使得其Smyth幂空间和Scott幂空间都不是强d-空间。该例子对幂空间构造下强良滤性和强R空间性质的保持问题给出了否定回答。此外，对于两点离散空间\ wo，在逐点收敛、紧开拓扑、Isbell拓扑、核开拓扑或Scott拓扑下，函数空间(\ wo,X)都不是强d-空间，其中Scott拓扑由逐点序诱导。
英文摘要：
Strong well-filteredness is a refinement of well-filteredness arising naturally in non-Hausdorff topology and domain theory. In this paper, we construct a countable locally compact strong R-space X such that neither its Smyth power space nor its Scott power space is a strong d-space. This example gives negative answers to the questions concerning the preservation of strong well-filteredness and the strong R-space property under power space constructions. Furthermore, for the two-point discrete space \two, the function space (\two,X) is not a strong d-space under any of the pointwise convergence, compact-open, Isbell, core-open or Scott topologies, where the Scott topology is induced by the pointwise order.
