In point set topology, it is well known that the Kuratowski 14-set problem is one of the most interesting results. In this note, we first give a brief survey of the Kuratowski’s theorem. In particular, we will study ...In point set topology, it is well known that the Kuratowski 14-set problem is one of the most interesting results. In this note, we first give a brief survey of the Kuratowski’s theorem. In particular, we will study and investigate the structure of the boundary of a given subset in a topological space. Some new results and topics which are related to the theorem of Kuratowski are presented and discussed. Finally, we pose some open problems of Kuratowskitype.展开更多
在不需要紧性假设下,利用拟C-凸函数及回收锥的性质,建立了向量优化问题有效点集的稳定性,获得了一列目标函数和可行集均扰动情形下的向量优化问题与对应的向量优化问题有效点集的Painlevé-Kuratowski内收敛性结果。所得结果推广...在不需要紧性假设下,利用拟C-凸函数及回收锥的性质,建立了向量优化问题有效点集的稳定性,获得了一列目标函数和可行集均扰动情形下的向量优化问题与对应的向量优化问题有效点集的Painlevé-Kuratowski内收敛性结果。所得结果推广和改进了相关文献(Attouch H,RiahiH.Stability results for Ekeland’s-variational principle and cone extremal solution;Huang X X.Stabilityin vector-valued and set-valued optimization)中的相应结果,并给出例子说明了所得结果的正确性。展开更多
文摘In point set topology, it is well known that the Kuratowski 14-set problem is one of the most interesting results. In this note, we first give a brief survey of the Kuratowski’s theorem. In particular, we will study and investigate the structure of the boundary of a given subset in a topological space. Some new results and topics which are related to the theorem of Kuratowski are presented and discussed. Finally, we pose some open problems of Kuratowskitype.
文摘在不需要紧性假设下,利用拟C-凸函数及回收锥的性质,建立了向量优化问题有效点集的稳定性,获得了一列目标函数和可行集均扰动情形下的向量优化问题与对应的向量优化问题有效点集的Painlevé-Kuratowski内收敛性结果。所得结果推广和改进了相关文献(Attouch H,RiahiH.Stability results for Ekeland’s-variational principle and cone extremal solution;Huang X X.Stabilityin vector-valued and set-valued optimization)中的相应结果,并给出例子说明了所得结果的正确性。