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Proceedings of the American Mathematical Society
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
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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?)

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  • [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 (36 #840)
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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0556632-0
PII: S 0002-9939(1980)0556632-0
Article copyright: © Copyright 1980 American Mathematical Society