A strengthening of a lemma on continuous families of closed convex sets (Q1188373)
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scientific article; zbMATH DE number 40545
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A strengthening of a lemma on continuous families of closed convex sets |
scientific article; zbMATH DE number 40545 |
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A strengthening of a lemma on continuous families of closed convex sets (English)
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13 August 1992
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Summary: Let \(X\) be a normed linear space and \(E(\cdot)\) a family of set-valued mappings on a metric space \(T\). It will be shown the following strengthening of a result by \textit{S. Rolewicz} [Funktionalanalysis und Steuerungstheorie (1976; Zbl 0333.49002), p. 174]. If \(E(\cdot)\) is lower semi-continuous in \(t_ 0\) and \(0\subset\text{int }E(t_ 0)\), then \(0\subset\text{int }E(t)\) holds for sufficiently neighbouring \(t\) of \(t_ 0\), too.
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