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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
DOI: https://doi.org/10.1090/S0002-9939-1976-0435805-0
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.


References [Enhancements On Off] (What's this?)

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  • [2] -, Normal solvability and the Fredholm alternative for mappings into infinite dimensional manifolds, J. Functional Analysis 8 (1971), 250-274. MR 44 #5834. MR 0288638 (44:5834)
  • [3] J. Daneš, A geometric theorem useful in nonlinear functional analysis, Boll. Un. Mat. Ital. (4) 6 (1972), 369-375. MR 47 #5678. MR 0317130 (47:5678)
  • [4] R. H. Martin, Jr., Approximation and existence of solutions to ordinary differential equations in Banach spaces, Funkcial. Ekvac. 16 (1973), 195-211. MR 50 #5128. MR 0352641 (50:5128)
  • [5] R. R. Phelps, Support cones in Banach spaces and their applications, Advances in Math. 13 (1974), 1-19. MR 49 #3505. MR 0338741 (49:3505)

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DOI: https://doi.org/10.1090/S0002-9939-1976-0435805-0
Article copyright: © Copyright 1976 American Mathematical Society

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