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| Lipschitz函数空间中的端点和圆点 |
| Extreme Points And Rotund Points in The Space of Lipschitz Functions |
| 投稿时间：2025-07-19 修订日期：2025-11-01 |
| DOI： |
| 中文关键词: Lipschitz函数空间 端点 圆点 强端点 |
| 英文关键词: Lipschitz function spaces extreme points rotund points strongly extreme points |
| 基金项目:2023年度高校科研计划项目（自然科学类) |
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| 中文摘要: |
| 本文对Lipschitz函数空间中的端点和圆点进行了深入研究。首先,给出了Lipschitz函数空间单位球面端点的等价特征定理的证明,并建立了Lipschitz对偶空间与赋范线性空间中端点之间的联系。通过分析Lipschitz函数的性质,证明了单位球面上端点集的补集是稠密的,而端点集本身并不稠密。此外,探讨了Lipschitz强端点的性质,指出在特定空间中,端点与强端点是等价的。研究结果丰富了Lipschitz函数空间的几何理论,并为后续研究提供了理论基础。 |
| 英文摘要: |
| This paper delves into the endpoints and zeros in the Lipschitz function space. It begins by proving the equivalent characteristic theorem for the endpoints of the unit sphere in the Lipschitz function space and establishes a connection between the Lipschitz dual space and the endpoints in normed linear spaces. By analyzing the properties of Lipschitz functions, it is shown that the complement of the set of endpoints on the unit sphere is dense, whereas the set of endpoints itself is not. Furthermore, the paper explores the properties of Lipschitz strong endpoints, noting that in specific spaces, endpoints and strong endpoints are equivalent. The findings enrich the geometric theory of Lipschitz function spaces and provide a theoretical foundation for future research. |
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