发表机构
Department of Mathematics, Shimane University（岛根大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究割点与非割点的Whitney性质，证明岸点性质在可精化映射下保持，并指出块点、非岸点及强中心点非Whitney可逆，相关连续统类无公共模型。
AI 中文摘要
本文研究了关于割点与非割点的若干性质。首先，我们证明了完全由岸点组成的连续统这一性质在可精化映射下得以保持。其次，我们证明了具有块点、具有非岸点以及具有强中心点均不是Whitney可逆性质。因此，文献[nonweak]中的问题2.9得到否定回答。此外，我们证明了对于这三个性质，见证序列强Whitney可逆性失效的连续统类均不存在公共模型。最后，结合余局部连通性不是Whitney可逆性质这一事实，我们证明了具有割点且每个正Whitney水平均为余局部连通的非无环连续统类没有公共模型。
英文摘要
In this paper, we study several properties concerning cut points and non-cut points. First, we show that the property of being a continuum consisting entirely of shore points is preserved under refinable maps. Next, we show that having a block point, having a non-shore point, and having a strong center point are not Whitney-reversible properties. Consequently, \cite[Question 2.9]{nonweak} has a negative answer. Furthermore, we show that none of the classes of continua witnessing the failure of the sequential strong Whitney-reversible property for these three properties admits a common model. Finally, in connection with the fact that colocal connectedness is not a Whitney-reversible property, we show that the class of nonaposyndetic continua having a cut point and such that every positive Whitney level is colocally connected has no common model.
