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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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


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.
    S. Banach, Théorème sur les ensembles de première categorie, Fund. Math. 16 (1930), 395-398.
  • K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
  • 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
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 78 (1980), 555-558
  • MSC: Primary 52A30; Secondary 46B99, 52A07, 54C50
  • DOI:
  • MathSciNet review: 556632