Abstract
Let $CC(X)$ be the collection of all non-empty compact, convex subsets of a complex Banach space $X$ endowed with the usual Hausdorff metric $h$. We shall define a natural weak topology ${\cal T}_w$ on $CC(X)$ and investigate properties of ${\cal T}_w$-convergent sequences. Our main result is a theorem which states that if $A_n$, $A\in CC(X)$ and $A_n$ is ${\cal T}_w$-convergent to $A$, then there exists a sequence $\{B_n\}$ (each $B_n$ is a finite convex combination of $A_k$'s) such that $B_n$ converges to $A$ with respact to the Hausdorff metric $h$.
Citation
Thakyin Hu. Jui-Chi Huang. "WEAK AND STRONG CONVERGENCE IN THE HYPERSPACE CC(X)." Taiwanese J. Math. 12 (5) 1285 - 1291, 2008. https://doi.org/10.11650/twjm/1500574263
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