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zbMATH Open
Article . 1998
Data sources: zbMATH Open
Journal of Applied Analysis
Article . 1998 . Peer-reviewed
Data sources: Crossref
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Contrasting Symmetric Porosity and Porosity

Contrasting symmetric porosity and porosity
Authors: Evans, M. J.; Humke, P. D.;

Contrasting Symmetric Porosity and Porosity

Abstract

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 \(x\in E\), \(\text{sp} (E,x)=p\).

Keywords

Classification of real functions; Baire classification of sets and functions, porosity, symmetric porosity

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
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