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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

New proof of a density theorem for the boundary of a closed set


Author: Peter Volkmann
Journal: Proc. Amer. Math. Soc. 60 (1976), 369-370
MSC: Primary 46B05
MathSciNet review: 0435805
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Abstract: From Browder [1] the following theorem is known: Let F be a closed subset of the Banach space E; then the set R of points $ x \in \partial F$, such that $ F \cap C = \{ x\} $ for at least one convex C with nonempty interior, is dense in $ \partial F$. A proof of this will be given by means of a theorem of Martin [4] on ordinary differential equations.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0435805-0
PII: S 0002-9939(1976)0435805-0
Article copyright: © Copyright 1976 American Mathematical Society