A selection theorem for multifunctions
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- by H. Sarbadhikari PDF
- Proc. Amer. Math. Soc. 71 (1978), 285-288 Request permission
Abstract:
In this paper the following theorem is proved. X is any set, H is a family of subsets of X which is $\lambda$-additive, $\lambda$-multiplicative and satisfies the $\lambda$-WRP for some cardinal $\lambda > {\aleph _0}$. Suppose Y is a regular Hausdorff space of topological weight $\leqslant \lambda$ such that given any family of open sets, there is a subfamily of cardinality $< \lambda$ with the same union. Let $F:X \to {\mathbf {C}}(Y)$, where ${\mathbf {C}}(Y)$ is the family of nonempty compact subsets of Y, satisfy $\{ x:F(x) \cap C \ne \emptyset \} \in {\mathbf {H}}$ for any closed subset C of Y. Then F admits a ${({\mathbf {H}} \cap {{\mathbf {H}}^c})_\lambda }$ measurable selector.References
- A. Maitra and B. V. Rao, Selection theorems for partitions of Polish spaces, Fund. Math. 93 (1976), no. 1, 47–56. MR 493956, DOI 10.4064/fm-93-1-47-56
- Maurice Sion, On uniformization of sets in topological spaces, Trans. Amer. Math. Soc. 96 (1960), 237–245. MR 131506, DOI 10.1090/S0002-9947-1960-0131506-X
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 71 (1978), 285-288
- MSC: Primary 54C65; Secondary 04A20, 54A25, 54C60
- DOI: https://doi.org/10.1090/S0002-9939-1978-0500507-0
- MathSciNet review: 500507