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Zeitschrift für Analysis und ihre Anwendungen

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Volume 22, Issue 3, 2003, pp. 505–516
DOI: 10.4171/ZAA/1158

Published online: 2003-09-30

Michael Selection Problem in Hyperconvex Metric Spaces

Xian Wu[1]

(1) Yunnan Normal University, Kunming, China

The Michael selection problem is researched in hyperconvex metric spaces. Our results show that the answer is "yes" for hyperconvex metric spaces and that the lower semicontinuity of the multi-valued mapping can be weakened. Moreover, as an application of our selection theorem, a fixed point theorem for locally-uniform weak lower semicontinuous multi-valued mappings is given.

Keywords: Hyperconvex metric spaces, lower semicontinuity, sub-admissable sets, quasi-lower semicontinuity, locally-uniform weak lower semicontinuity

Wu Xian: Michael Selection Problem in Hyperconvex Metric Spaces. Z. Anal. Anwend. 22 (2003), 505-516. doi: 10.4171/ZAA/1158