Upper porous sets which are not \(\sigma\)-lower porous (Q987911)
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scientific article; zbMATH DE number 5778783
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Upper porous sets which are not \(\sigma\)-lower porous |
scientific article; zbMATH DE number 5778783 |
Statements
Upper porous sets which are not \(\sigma\)-lower porous (English)
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2 September 2010
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Let \(g_i:[0,+\infty[\rightarrow\mathbb{R}\) be increasing continuous functions such that \(g_i(0)=0\) and \(g_i(x)>x\) in a neighbourhood of \(0\). The main result says that any topologically complete metric space without isolated points contains a closed (\(g_1\))-shell porous set which is not \(\sigma\)-(\(g_2\))-lower porous. This improves a result contained in [\textit{L. Zajíček}, Abstr. Appl. Anal. 2005, No. 5, 509--534 (2005; Zbl 1098.28003)]
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upper porosity
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lower porosity
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shell porosity
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