On closed starshaped sets and Baire category
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- by Gerald Beer PDF
- Proc. Amer. Math. Soc. 78 (1980), 555-558 Request permission
Abstract:
Let C be a closed set of second category in a normed linear space, and let ${C^\ast }$ be the subset of C each point of which sees all points of C except a set of first category. If ${C^\ast }$ is nonempty, then ${C^\ast }$ is a closed convex set. Moreover, $C = K \cup P$ where K is a closed starshaped set with convex kernel ${C^\ast }$ and P is a set of first category.References
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S. Banach, Théorème sur les ensembles de première categorie, Fund. Math. 16 (1930), 395-398.
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- John C. Oxtoby, Measure and category, 2nd ed., Graduate Texts in Mathematics, vol. 2, Springer-Verlag, New York-Berlin, 1980. A survey of the analogies between topological and measure spaces. MR 584443
- Frederick A. Valentine, Convex sets, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Toronto-London, 1964. MR 0170264
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 78 (1980), 555-558
- MSC: Primary 52A30; Secondary 46B99, 52A07, 54C50
- DOI: https://doi.org/10.1090/S0002-9939-1980-0556632-0
- MathSciNet review: 556632