Geodesic
An analogy of Hahn-Banach separation theorem for nearly topological linear spaces
Ural mathematical journal, Tome 7 (2021) no. 1, pp. 81-86

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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.
Keywords: Hahn-Banach separation theorem, $\alpha$-open sets, $\alpha$-compact sets, nearly topological linear spaces. 
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Madhu Ram. An analogy of Hahn-Banach separation theorem for nearly topological linear spaces. Ural mathematical journal, Tome 7 (2021) no. 1, pp. 81-86. http://geodesic.mathdoc.fr/item/UMJ_2021_7_1_a5/