The AMS website will be down for maintenance on May 23 between 6:00am - 8:00am EDT. For questions please contact AMS Customer Service at or (800) 321-4267 (U.S. & Canada), (401) 455-4000 (Worldwide).


Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



On closed starshaped sets and Baire category

Author: Gerald Beer
Journal: Proc. Amer. Math. Soc. 78 (1980), 555-558
MSC: Primary 52A30; Secondary 46B99, 52A07, 54C50
MathSciNet review: 556632
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

  • [1] S. Banach, Théorème sur les ensembles de première categorie, Fund. Math. 16 (1930), 395-398.
  • [2] K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. MR 0217751
  • [3] 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
  • [4] Frederick A. Valentine, Convex sets, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Toronto-London, 1964. MR 0170264

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 52A30, 46B99, 52A07, 54C50

Retrieve articles in all journals with MSC: 52A30, 46B99, 52A07, 54C50

Additional Information

Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society