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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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2025-01-01
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| Series: | Categories and General Algebraic Structures with Applications |
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| Online Access: | https://cgasa.sbu.ac.ir/article_104792_2c8340ceab54f22f6cb46e3e5ad65574.pdf |
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| _version_ | 1832586949772181504 |
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| author | Paranjothi Pillay Dharmanand Baboolal |
| author_facet | Paranjothi Pillay Dharmanand Baboolal |
| author_sort | Paranjothi Pillay |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a2b7554478304f38b6dcf4f2064f8e94 |
| institution | Kabale University |
| issn | 2345-5853 2345-5861 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Shahid Beheshti University |
| record_format | Article |
| series | Categories and General Algebraic Structures with Applications |
| spelling | doaj-art-a2b7554478304f38b6dcf4f2064f8e942025-01-24T18:43:40ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612025-01-0122113915510.48308/cgasa.2024.235538.1489104792Uniform Lipschitz-connectedness and metric convexityParanjothi Pillay0Dharmanand Baboolal1Department of Mathematics and Applied Mathematics University of the Western Cape South AfricaSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4000, South Africa.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.https://cgasa.sbu.ac.ir/article_104792_2c8340ceab54f22f6cb46e3e5ad65574.pdfmetric spacelipschitz-connecteduniformly lipschitz connectedproper metric spacedilatationsuniversal lipschitz constant |
| spellingShingle | Paranjothi Pillay Dharmanand Baboolal Uniform Lipschitz-connectedness and metric convexity Categories and General Algebraic Structures with Applications metric space lipschitz-connected uniformly lipschitz connected proper metric space dilatations universal lipschitz constant |
| title | Uniform Lipschitz-connectedness and metric convexity |
| title_full | Uniform Lipschitz-connectedness and metric convexity |
| title_fullStr | Uniform Lipschitz-connectedness and metric convexity |
| title_full_unstemmed | Uniform Lipschitz-connectedness and metric convexity |
| title_short | Uniform Lipschitz-connectedness and metric convexity |
| title_sort | uniform lipschitz connectedness and metric convexity |
| topic | metric space lipschitz-connected uniformly lipschitz connected proper metric space dilatations universal lipschitz constant |
| url | https://cgasa.sbu.ac.ir/article_104792_2c8340ceab54f22f6cb46e3e5ad65574.pdf |
| work_keys_str_mv | AT paranjothipillay uniformlipschitzconnectednessandmetricconvexity AT dharmanandbaboolal uniformlipschitzconnectednessandmetricconvexity |