New proof of a density theorem for the boundary of a closed set
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- by Peter Volkmann PDF
- Proc. Amer. Math. Soc. 60 (1976), 369-370 Request permission
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
- Felix E. Browder, On the Fredholm alternative for nonlinear operators, Bull. Amer. Math. Soc. 76 (1970), 993–998. MR 265999, DOI 10.1090/S0002-9904-1970-12527-7
- Felix E. Browder, Normal solvability and the Fredholm alternative for mappings into infinite dimensional manifolds, J. Functional Analysis 8 (1971), 250–274. MR 0288638, DOI 10.1016/0022-1236(71)90012-7
- Josef Daneš, A geometric theorem useful in nonlinear functional analysis, Boll. Un. Mat. Ital. (4) 6 (1972), 369–375 (English, with Italian summary). MR 0317130
- Robert H. Martin Jr., Approximation and existence of solutions to ordinary differential equations in Banach spaces, Funkcial. Ekvac. 16 (1973), 195–211. MR 352641
- R. R. Phelps, Support cones in Banach spaces and their applications, Advances in Math. 13 (1974), 1–19. MR 338741, DOI 10.1016/0001-8708(74)90062-0
Additional Information
- © Copyright 1976 American Mathematical Society
- 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