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Zeitschrift für Analysis und ihre Anwendungen


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Volume 10, Issue 3, 1991, pp. 415–416
DOI: 10.4171/ZAA/463

Published online: 1991-09-30

A Strengthening of a Lemma on Continuous Families of Closed Convex Sets

Rolf Klötzler[1]

(1) Borsdorf, Germany

Let $X$ be a normed linear space and $E(\cdot)$ a family of set-valued mappings on a metric space $T$. lt will be shown the following strengthening of a result by S. Rolewicz. If $E(\cdot)$ is lower semi-continuous in $t_o$ and $O c$ int $E(t_o)$, then $O c$ int $E(t)$ holds for sufficiently neighbouring $t$ of $t_o$ too.

Keywords: Semi-continuous set-valued mapping, interior points

Klötzler Rolf: A Strengthening of a Lemma on Continuous Families of Closed Convex Sets. Z. Anal. Anwend. 10 (1991), 415-416. doi: 10.4171/ZAA/463