Honam Mathematical Journal (호남수학학술지)

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A MISCELLANY OF SELECTION THEOREMS WITHOUT CONVEXITY

  • Kim, Hoonjoo (Department of mathematics education, Sehan University)
  • Received : 2013.10.14
  • Accepted : 2013.11.20
  • Published : 2013.12.25
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Abstract

In this paper, we give sufficient conditions for a map with nonconvex values to have a continuous selection and the selection extension property in LC-metric spaces under the one-point extension property. And we apply it to weakly lower semicontinuous maps and generalize previous results. We also get a continuous selection theorem for almost lower semicontinuous maps with closed sub-admissible values in $\mathbb{R}$-trees.

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References

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