ISSN: 2310-757X
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http://elar.urfu.ru/handle/10995/108592| Title: | An Analogy of Hahn-Banach Separation Theorem |
| Authors: | Ram, M. |
| Issue Date: | 2021 |
| Publisher: | N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences Ural Federal University named after the first President of Russia B.N. Yeltsin |
| Citation: | Ram M. An Analogy of Hahn-Banach Separation Theorem / M. Ram. — DOI 10.15826/umj.2021.1.006. — Text : electronic // Ural Mathematical Journal. — 2021. — Volume 7. — № 1. — P. 81-86. |
| Abstract: | In this paper, we introduce the notion of nearly topological linear spaces and use it to formulate an alternative definition of the Hahn–Banach separation theorem. We also give an example of a topological linear space to which the result is not valid. It is shown that R with its ordinary topology is not a nearly topological linear space. |
| Keywords: | HAHN–BANACH SEPARATION THEOREM Α-OPEN SETS Α-COMPACT SETS NEARLY TOPOLOGICAL LINEAR SPACES |
| URI: | http://elar.urfu.ru/handle/10995/108592 |
| Access: | Creative Commons Attribution License |
| License text: | https://creativecommons.org/licenses/by/4.0/ |
| ISSN: | 2414-3952 |
| DOI: | 10.15826/umj.2021.1.006 |
| metadata.dc.description.sponsorship: | The author thanks the referee and the reviewers for their valuable comments/suggestions which improved the quality of the paper. |
| Origin: | Ural Mathematical Journal. 2021. Volume 7. № 1 |
| Appears in Collections: | Ural Mathematical Journal |
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| umj_2021_7_1_81-86.pdf | 104 kB | Adobe PDF | View/Open |
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