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An analogy of Hahn-Banach separation theorem for nearly topological linear spaces
Madhu Ram University of Jammu
Аннотация:
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 $\mathbb{R}$ with its ordinary topology is not a nearly topological linear space.
Ключевые слова:
Hahn-Banach separation theorem, $\alpha$-open sets, $\alpha$-compact sets, nearly topological linear spaces.
Образец цитирования:
Madhu Ram, “An analogy of Hahn-Banach separation theorem for nearly topological linear spaces”, Ural Math. J., 7:1 (2021), 81–86
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/umj138 https://www.mathnet.ru/rus/umj/v7/i1/p81
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Страница аннотации: | 99 | PDF полного текста: | 54 | Список литературы: | 25 |
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