The set of noncontractive mappings is \(\sigma\)-porous in the space of all nonexpansive mappings (Q2756225)
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scientific article; zbMATH DE number 1672761
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The set of noncontractive mappings is \(\sigma\)-porous in the space of all nonexpansive mappings |
scientific article; zbMATH DE number 1672761 |
Statements
16 December 2002
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smallness
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\(\sigma\)-porosity
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nullset
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set of first category
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The set of noncontractive mappings is \(\sigma\)-porous in the space of all nonexpansive mappings (English)
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There exist several notions which make it possible to measure the ``smallness'' of a set, the most important ones being a nullset or a set of first category. A stronger notion is that of \(\sigma\)-porosity. Sharpening a previous result in C. R. Acad. Sci. Canada 22, No. 3, 118-124 (2000; Zbl 0971.47039), the authors show that the set of all nonexpansive maps on a fixed bounded closed convex set which are not contractive is \(\sigma\)-porous.
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