Approximate selections and fixed points for upper semicontinuous maps with decomposable values

Cellina, Arrigo; Colombo, Giovanni; Fonda, Alessandro

doi:10.1090/S0002-9939-1986-0861771-6

Approximate selections and fixed points for upper semicontinuous maps with decomposable values
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by Arrigo Cellina, Giovanni Colombo and Alessandro Fonda

Proc. Amer. Math. Soc. 98 (1986), 663-666

DOI: https://doi.org/10.1090/S0002-9939-1986-0861771-6

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Abstract:

We prove the existence of continuous approximate selections of upper semicontinuous maps from a separable locally compact metric space $S$ into the decomposable subsets of ${L^1}(T,Z)$. We then extend a fixed point theorem of Kakutani to upper semicontinuous maps with decomposable values.

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