AN ANALOGY OF HAHN–BANACH SEPARATION THEOREM FOR NEARLY TOPOLOGICAL LINEAR SPACES
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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.
1969 ◽
Vol 66
(3)
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pp. 541-545
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1965 ◽
Vol 5
(1)
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pp. 25-35
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1967 ◽
Vol 63
(2)
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pp. 311-313
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1972 ◽
Vol 72
(1)
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pp. 7-9
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1988 ◽
Vol 11
(3)
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pp. 585-588
1989 ◽
Vol 106
(2)
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pp. 277-280
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1972 ◽
Vol 72
(1)
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pp. 37-47
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1968 ◽
Vol 64
(2)
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pp. 335-340
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