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Contrasting symmetric porosity and porosity. (English) Zbl 0922.26003
The aim of the paper is to compare the behaviour of sets with respect to symmetric porosity and porosity. The authors have found several similarities as well as several differences. As an example of the first let us quote the following Theorem: If $$0< p<1$$ and $$E$$ is a closed, $$p$$-symmetrically porous set, then there exists a number $$q$$, $$p< q<1$$, such that the set $$\{x\in E: \text{sp} (E,x)\geq q\}$$ is residual in $$E$$. The difference is exhibited in the following example: Given $$0< p<1$$, there exists a $$G_\delta$$ set $$E\subset [0,1]$$ such that for each $$x\in E$$, $$\text{sp} (E,x)=p$$.

##### MSC:
 26A21 Classification of real functions; Baire classification of sets and functions
##### Keywords:
symmetric porosity; porosity
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##### References:
 [1] Evans M.J., Real Anal. Exchange 17 pp 809– (1991) [2] Evans M.J., Real Anal. Exchange 17 pp 820– (1991) [3] Evans M.J., Real Anal. Exchange 17 pp 258– (1991) [4] Evans M.J., Czechoslovak Math. J. 44 pp 251– (1994) [5] Evans M.J., Proc. Amer. Math. Soc. 122 pp 805– (1994) [6] Gruber P.M., Mh. Math. 108 pp 149– (1989) · Zbl 0666.28005 [7] Repický M., Real Anal. Exchange 17 pp 416– (1991) [8] Vallin R.W., Real Anal. Exchange 18 pp 294– (1992) [9] Zajíček L., Mat. 101 pp 350– (1976) [10] Zajíček L., Real Anal. Exchange 13 pp 314– (1987) [11] Zajíček L., Atti Sem. Mat. Fis. Univ. Modena 41 pp 263– (1993)
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