How many sets are porous?

Zamfirescu, Tudor

doi:10.1090/S0002-9939-1987-0884484-4

How many sets are porous?
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by Tudor Zamfirescu

Proc. Amer. Math. Soc. 100 (1987), 383-387

DOI: https://doi.org/10.1090/S0002-9939-1987-0884484-4

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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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Topologie

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