| 李国强,余淑辉.模糊度量空间的强嵌入*[J].数学年刊A辑,2022,43(4):399~414 |
| 模糊度量空间的强嵌入* |
| Strong Embeddability for Fuzzy Metric Spaces |
| Received:June 13, 2021 Revised:October 10, 2022 |
| DOI：10.16205/j.cnki.cama.2022.0026 |
| 中文关键词: 粗几何, 模糊度量空间, 强嵌入, 粗拓扑 |
| 英文关键词:Coarse geometry, Fuzzy metric spaces, Strong embeddability,Coarse topology |
| 基金项目:2023年度贵州省教育厅高校科学研究项目(青年项目)(No.黔教技[2022]172)和2022年度贵州财经大学校级项目(No.2022KYQN12) |
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| 中文摘要: |
| 本文定义了George 和Veeramani 意义下的模糊度量空间的强嵌入,证明了可强嵌入的模糊度量空间能够粗嵌入到Hilbert空间.另外还证明了强嵌入在模糊度量空间的粗范畴下是不变的,并给出了模糊度量空间强嵌入的一些等价刻画. |
| 英文摘要: |
| In this paper, the authors define strong embeddability of fuzzy metric spaces in the sense of George and Veeramani, and prove that fuzzy metric spaces with strong embeddability are coarsely embeddable into Hilbert space. The authors also show that strong embeddability is an invariant in the coarse category of fuzzy metric spaces. Furthermore,the authors provide equivalent characterizations of strong embeddability for fuzzy metric spaces. |
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