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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

How many sets are porous?


Author: Tudor Zamfirescu
Journal: Proc. Amer. Math. Soc. 100 (1987), 383-387
MSC: Primary 54E50; Secondary 46B20, 54E52
MathSciNet review: 884484
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Abstract: The notion of a $ \sigma $-porous set is often used to sharpen results on sets of first Baire category or of measure zero. It essentially uses the related notion of porosity. We find out in this note that there are quite a few porous sets: In complete convex metric spaces, most totally bounded closed sets are porous! Then we strengthen this result for the case of a Banach space.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0884484-4
PII: S 0002-9939(1987)0884484-4
Article copyright: © Copyright 1987 American Mathematical Society