Strongly proximinal subspaces of finite codimension in $C(K)$
Volume 109 / 2007
Colloquium Mathematicum 109 (2007), 119-128
MSC: 41A65, 46B20.
DOI: 10.4064/cm109-1-10
Abstract
We characterize strongly proximinal subspaces of finite codimension in $C(K)$ spaces. We give two applications of our results. First, we show that the metric projection on a strongly proximinal subspace of finite codimension in $C(K)$ is Hausdorff metric continuous. Second, strong proximinality is a transitive relation for finite-codimensional subspaces of $C(K)$.
