Abstract
In [1] Tukey proves that if A and B are closed convex subsets in a Banach space, so that A is bounded and A-B is dense in the open unit ball U then A-B⊃U. We shall give here a more general result than the former one which contains the Banach's isomorphism theorem as particular case. Other results over convex sets are also given.
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TUKEY, J.W.: Some notes on the separation of convex sets. Port. Math.3, 95–102 (1942)
VALDIVIA, M.: Absolutely convex sets in barrelled spaces. Ann. Inst. Fourier21, 2, 3–13 (1971)
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The author is indebted to the referee for the several very valuable comments.
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Valdivia, M. Some notes on convex sets. Manuscripta Math 26, 381–386 (1979). https://doi.org/10.1007/BF01170262
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DOI: https://doi.org/10.1007/BF01170262