Abstract
Let $X$ be a separable Banach space, $Y$ a closed, nonreflexive, linear subspace, and $P$ the set of points admitting a nearest approximation in $Y$. Then $P$ is an analytic set, and has three obvious algebraic properties. By adjusting the norm of $X$, any analytic set of this kind can be realized as the set of elements proximal to $Y$.
Citation
Robert Kaufman. "Descriptive theory of nearest points in Banach spaces." Illinois J. Math. 54 (3) 1157 - 1162, Fall; 2010. https://doi.org/10.1215/ijm/1336049988
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