Uniform Lipschitz-connectedness and metric convexity
In this paper we continue with our study of uniformly Lipschitz-connected metric spaces. We obtain further properties of uniformly Lipschitz-connected metric spaces and then obtain a generalisation of a result due to Edelstein. In addition, we show that for a proper Lipschitz-connected metric spa...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Shahid Beheshti University
2025-01-01
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| Series: | Categories and General Algebraic Structures with Applications |
| Subjects: | |
| Online Access: | https://cgasa.sbu.ac.ir/article_104792_2c8340ceab54f22f6cb46e3e5ad65574.pdf |
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| Summary: | In this paper we continue with our study of uniformly Lipschitz-connected metric spaces. We obtain further properties of uniformly Lipschitz-connected metric spaces and then obtain a generalisation of a result due to Edelstein. In addition, we show that for a proper Lipschitz-connected metric space, $L_d = 1$ precisely when $X$ is convex, which leads us to conjecture that $L_d$ is a kind of measure of convexity in a proper Lipschitz-connected metric space. We provide some examples to corroborate our conjecture. |
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| ISSN: | 2345-5853 2345-5861 |